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QUARTZ  OPERATOR'S 


HAND  BOOK. 


WHEELER  &  RANDALL. 


SAN  FRANCISCO: 

Mining  and  Scientific  Press  Job  Printing  Office. 

1865. 


I 


Ibwry 

QUARTZ  OPERATOR'S  HAND  ROOK. 


In  the  preparation  of  this  Hand  Book,  the  object 
has  been  to  make  it  a  reliable  and  practical  guide  to  the 
Quartz  Operator. 

No  pains  have  been  spared  in  gathering  the  material 
and  in  rendering  the  subjects  discussed  as  concise  and 
plain  as  their  nature  would  admit. 

Mindful  that  science  and  practice  go  hand  in  hand, 
the  authors  have  confined  their  investigations  to  useful 
and  established  facts,  leaving  untouched  all  that  is 
doubtful  and  chimerical. 

No  claim  is  made  to  originality,  unless  it  may  be  in 
regard  to  the  discussion  of  the  tractory  and  the  grind- 
ing effects  of  differently  formed  plates  —  a  subject  of 
great  importance  to  every  quartz  miner. 

To  what  extent  the  authors  have  succeeded  in  their 
object,  is  submitted  with  no  little  diffidence  to  the  decis- 
ion of  the  public. 

WHEELER  &  RANDALL. 

San  Francisco,  April  26,  1865. 


4  QUARTZ    OPERATOR'S 

BLOWPIPE. 

The  Blowpipe  is  an  instrument  used  for  directing,  by 
a  current  of  air,  the  flame  of  a  lamp  or  candle  upon  a 
mineral  substance  to  fuse  or  oxydize  it.  The  flame 
consists  essentially  of  two  parts — the  oxydizing  and 
reducing. 

1st.  The  oxydizing  part  is  the  outer  and  slightly 
luminous  flame. 

2nd.  The  reducing  part,  which  is  hottest,  is  the  inner 
blue  flame. 

The  reagents  mostly  used  in  making  blowpipe  tests 
are  charcoal,  carbonate  of  soda,  cyanide  of  potassium 
and  borax. 

The  charcoal  performs  the  part  of  a  cupel  as  well  as 
that  of  a  reagent.  The  best  charcoal  is  made  of 
young  hard  wood. 

The  cupel  or  support  consists  of  a  sound  piece  of 
coal  sawed  or  broken  lengthwise,  having  a  small  cavity 
made  in  its  plain  side  near  the  edge  to  hold  the  sub- 
stance to  be  tested. 

The  borax  is  prepared  by  being  melted  or  vitrified 
and  pulverized. 

(A)  Blowpipe  Assay  of  Silver  Ores  containing  sul- 
phur and  arsenic. 

1st.  Roast  the  pulverized  ore  within  a  shallow  cavity 
on  the  coal  support.  To  do  this,  direct  by  the  blowpipe 
the  oxydizing  flame,  that  is,  the  extreme  point  of  the 
outer  flame  upon  the  powdered  ore;  turn  the  specimen 


HAND    BOOK.  5 

occasionally  to  expose  all  of  its  parts  to  oxydation. 
Let  the  blast  at  first  be  gentle,  then  increased  and  con- 
tinued till  the  sulphurous  odors  cease. 

2nd.  Pulverize  the  roasted  ore  and  put  it  upon  the 
charcoal  within  a  prepared  cavity ;  cover  it  over  with 
carbonate  of  soda  and  direct  upon  it  the  reducing  flame, 
that  is,  the  inner  blue  flame;  let  the  blast  at  first  be 
gentle,  and  chiefly  employed  in  fusing  and  bringing  to- 
gether all  parts  of  the  flux,  then  increase  the  blast, 
shaking  the  support  or  coal,  so  as  to  gather  the  metal 
in  one  globule,  which  cool  and  extract  from  the  slag. 

3rd.  Cupel  the  button  thus  obtained,  adding  to  it  three 
parts  of  lead  in  a  bone-ash  cupel.  To  do  this,  employ 
the  oxydizing  flame  by  using  a  very  gentle  blast. 

Cool,  weigh  the  button  and  compare  its  weight  with 
that  of  the  original  ore. 

(B)  Place  within  the  cavity,  on  the  charcoal,  a  mix- 
ture of 

Powdered  Ore,  (not  necessarily  roasted) .  .    1  part. 

Borax- Glass,  (pulverized) 1     " 

Lead,  (Litharge  is  often  preferable) 3     " 

and  direct  upon  it  the  reducing  flame  till  all  the  metal 
is  gathered  in  one  button.  Let  the  blast  at  first  be 
gentle  and  chiefly  directed  to  the  borax,  then  increased 
and  continued  till  the  object  is  attained.  Extract  and 
cupel  the  button  as  in  example  (A.) 


BLOWPIPE    TESTS. 

"  When   common   borax   of  the  shops  is  heated,  it 

3a 


6  QUARTZ    OPERATOR'S 

forms,  at  first,  a  white  spongy  mass,  and  if  we  continue 
to  heat  it,  pressing  it  down  into  a  clay  or  Hessian 
crucible,  it  melts  at  a  brown-red  heat  into  a  clear  trans- 
parent glass.  This  glass,  when  powdered  fine,  is  the 
substance  which  we  make  use  of  in  blowpipe  experi- 
ments. When  we  heat  a  platinum  wire  to  redness,  and 
dip  it  into  powdered  borax,  it  will,  when  heated  again, 
form  a  globule  of  borax-glass  at  its  lower  extremity. 
This  globule  is  brought  in  contact  with  the  hot  specimen 
to  be  tested,  and  the  flame  applied ;  it  will  now  absorb 
some  of  the  hot  specimen,  dissolve  it,  and  show  by  its 
color  what  kind  of  mineral  is  under  examination. 

"  This  test  must  be  made  by  means  of  the  spirit  lamp 
or  alcohol  flame.  The  color  of  the  glass  formed,  when 
cold  or  warm,  when  in  the  oxydizing  part  of  the  flame, 
or  in  the  reducing  flame,  is,  in  many  cases,  a  decisive 
test,  if  it  forms  metal  in  the  latter,  or  merely  changes 
its  color. 

"Lime  is  infusible  by' itself,  but  gives  a  strong 
light ;  with  borax,  it  melts  into  a  colorless  glass.  It  is 
not  soluble  in  carbonate  of  soda.  Both,  when  heated 
together,  are  absorbed  by  the  charcoal.  Magnesia  acts 
like  lime.  Alumina  is  infusible  by  itself;  it  melts  with 
borax  into  a  colorless  glass,  and  if  much  alumina  is 
present  the  glass  is  opaque ;  carbonate  of  soda  does  not 
dissolve  this  substance. 

"  Oxyd  of  Antimony  sublimes  by  itself,  and  colors 
the  flame  a  greenish-blue ;  with  borax  it  forms  a  yellow 
glass  when  hot,  and  colorless  when  cold,  in  the  oxydiz- 


HAND    BOOK.  7 

ing  flame.  In  the  reducing  flame,  it  forms  a  gray, 
vitrious  mass  and  shrinks.  With  carbonate  of  soda,  or 
a  mixture  of  cyanide  of  potassium  and  soda,  it  forms  a 
metal  which  easily  evaporates  in  white  smoke  in  the 
flame.     The  metali  s  very  fusible  and  brittle. 

• "  Oxyd  of  Bismuth  is  fusible  and  forms  on  wire  a 
dark-brown  glass  while  hot,  and  a  yellow  glass  when 
cold ;  it  forms  metal  on  charcoal,  and  with  borax  it 
melts  into  a  colorless  bead.  With  carbonate  of  soda,  it 
forms  metal  on  a  coal  support. 

"  Oxyd  of  Chrome  does  not  change  in  the  flame  when 
alone ;  it  forms  with  borax  a  bead  which  is  red  while 
hot,  but  changes  into  green  when  cold  and  under  the 
oxydizing  influences ;  when  the  mixture  is  exposed  to 
the  reducing  flame  it  is  always  green.  With  carbonate 
of  soda  it  melts  to  a  dark-orange  glass  when  hot  and 
oxydized,  and  becomes  opaque  when  cold.  In  the 
reducing  flame  it  is  always  opaque  and  orange,  changing 
to  green  when  cold. 

"  Oxyd  of  Cobalt  is  unchangeable  by  itself,  but  it 
forms  a  characteristic  deep-blue  glass  with  borax.  It 
is  reduced  on  charcoal  when  mixed  with  carbonate  of 
soda,  forming  a  gray  magnetic  powder. 

"  Oxyd  of  Copper  fuses  in  the  oxydizing  flame ;  in 
the  reducing  flame  it  forms  metal ;  with  borax  it 
forms  a  green  glass  in  the  oxydizing  flame,  and  in  the 
reducing  flame  brown-red;  with  soda  it  is  reduced  on 
charcoal,  giving  malleable  metal. 

"  Per-  Oxyd  of  Iron  is  unchangeable  in  the  oxydizing 

4a 


8  QUARTZ    OPERATOR'S 

flame;  in  the  reducing  fire  it  blackens  and  becomes 
magnetic  oxyd.  It  forms  a  bright-red  glass  when  heated 
with  borax,  which  changes  to  a  pale  dirty-red  when 
cold,  in  the  oxydizing  flame ;  in  the  reducing  flame  it 
forms  a  bottle-green,  often  black-green  glass.  With 
soda  or  alkaline  flux,  it  forms  metal  on  the  charcoal 
support,  which  appears  as  a  dark  magnetic  powder. 

"  Oxyd  of  Lead  shows  at  first  a  clear  blue  flame,  after 
which  it  fuses  to  an  orange-yellow  glass ;  on  a  charcoal 
support  it  is  reduced  to  metal.  With  borax  it  forms  a 
yellow  glass  when  hot,  which  is  nearly  colorless  when 
cold.  When  this  oxyd  is  mixed  with  alkaline  flux,  it 
forms  metal  instantly  on  charcoal ;  in  the  alcohol  flame, 
on  wire,  it  forms  a  transparent  yellow  glass  with  car- 
bonate of  soda. 

"  Oxyd  of  Manganese  is  infusible  alone,  and  changes 
its  colors  to  brown ;  with  borax  it  melts  to  a  black  glass 
when  much  manganese  is  used ;  when  little  oxyd  and 
much  borax  are  melted  together  in  the  presence  of 
carbon,  the  result  is  an  amethyst  colored  glass,  and  if 
brought  within  the  reducing  flame  on  charcoal,  it  is 
colorless,  and  remains  so  when  quickly  cooled.  With  soda 
it  melts  to  an  opaque  green  glass  in  the  oxydizing  fire, 
and  on  a  foil  of  platinum.  This  test  is  characteristic  of 
manganese. 

"  Oxyd  of  Nichle  is  not  changed  by  heat;  with  borax 
it  melts  to  an  orange-red  glass,  which  is  almost  colorless 
when  cold.  In  the  reducing  flame,  on  charcoal,  this 
glass  becomes  gray;   this  color  is  caused  by  reduced 


HAND    BOOK.  9 

metal.  With  soda,  it  forms  a  magnetic  powder  of  metal 
on  charcoal. 

"  Oxyd  of  Silver  is  instantly  reduced  to  metal  when 
brought  within  the  flame.  It  forms  a  white  opaque 
glass  with  borax,  and  is  partly  reduced  to  metal  in  all 
instances  ;  with  alkaline  fluxes  it  forms  metal  directly, 
when  brought  in  the  flame. 

"Oxyd  of  Tellurium  imparts  to  the  flame  a  green 
color,  fuses  and  sublimes ;  on  charcoal  it  is  easily  re- 
duced to  metal.  With  borax,  it  melts  to  a  colorless 
glass  in  the  oxydizing  flame ;  in  the  reducing  flame  the 
glass  is  gray.  With  carbonate  of  soda  it  acts  as  with 
borax  but  less  distinctly. 

"  The  Oxyds  of  Tin  are  converted  into  sesqui-oxyd, 
becoming  dirty-yellow  in  the  oxydizing  flame ;  it  forms 
metal  after  protracted  heating  on  the  charcoal  support 
and  in  the  reducing  flame.  With  borax  it  forms  a  clear 
glass,  and  with  alkaline  fluxes  it  is  easily  reduced  to 
metal  on  charcoal. 

"Titanic  Acid  is  not  altered  in  the  flame  when  ex- 
posed to  it ;  with  borax  it  melts  to  a  colorless  glass, 
which  becomes  opaque  in  cooling.  In  the  reducing 
flame  it  becomes  first  yellow,  then  amethyst,  and  dark- 
ens in  cooling.  With  carbonate  of  soda  it  dissolves 
with  effervesence,  forming  a  faint  yellow  glass,  which 
becomes  gray  in  cooling.  It  forms  no  metal  on  char- 
coal. 

"Zinc. — The  oxyd  of  this  metal  forms  a  strong  whitish- 
green  flame ;    it  is  slightly  vellow  when  hot  but  turns 

5a 


10  QUARTZ    OPERATOR'S 

white  in  cooling.  With  borax  it  forms  a  transparent 
glass,  which  becomes  milky  by  an  intermittent  flame  5 
in  the  reducing  flame  it  forms  metal  .which  is  quickly 
evaporated.  Alkaline  fluxes  do  not  alter  it  in  the 
oxydizing  flame ;  it  is  reduced  on  charcoal,  and  in  the 
reducing  flame.  The  metal  burns  readily  and  forms  a 
white  floculent  oxyd,  which  is  yellow  when  hot." — 
Overman's  Treaties  on  Metallurgy,  pages  154 — 157. 


CHEMICAL    TESTS. 

Reagents  or  tests,  usually  in  liquid  form,  are  sub- 
stances for  indicating  the  presence  of  other  bodies.  In 
the  following  examples  the  reagents  are  arranged  at  the 
left  hand  side  of  the  page,  and  the  precipitates  or  pro- 
ducts at  the  right.  The  proper  solvents  are  indicated 
by  the  name  of  the  solution  holding  the  substances 
sought : 

TESTS  FOR  GOLD  IN  SOLUTION  WITH  AQUA-REGIA. 
Sulphate  of  Iron  gives ....   Metallic  Gold  as  a  purple 

powder. 

Oxalic  Acid  gives Metallic  Gold  in  large  flakes 

Potash  u      Yellow  Precipitate. 

Soda  "      "  " 

TESTS    FOR  SILVER   IN  SOLUTION  WITH  NITRIC  ACID. 

Potash  gives Dark-Olive  Precipitate. 

Soda         "      "        "  " 

Plate  of  Copper  gives  ....   Metallic  Silver. 
Muriatic  Acid        "     White,  Curdy  Precipitate. 


HAND    BOOK.  11 

Common  Salt  gives     ....   White  Curdy  Precipitate. 
Tincture  of  Nut-Gail  gives,  Brown  Precipitate. 

TESTS  FOR  COBALT  IN   SOLUTION  WITH  NITRIC  ACID. 

Potash  gives Blue  Precipitate. 

Soda  "     "  " 

Ferro-Prusiate    of    Potash 

gives Green        " 

Carbonate  of  Potash       "      Red  " 

TESTS  FOR  BISMUTH  IN  SOLUTION  WITH  NITRIC  ACID. 

Pure  Water  gives White  Precipitate. 

Gallic  Acid      "      Greenish  Yellow. 

Potash  "     White  Precipitate. 

Soda  "     "  " 

TESTS  FOR  LEAD  IN  SOLUTION  WITH  NITRIC  ACID. 
Sulphate  of  Soda  gives .  .  .   White  Precipitate. 
Sulphuric  Acid         "...        "  " 

Infusion  of  Nut- Gall  gives,       "  * 

TESTS  FOR  COPPER  IN   SOLUTION  WITH  NITRIC  ACID. 

Plate  of  Iron  gives Metallic  Copper. 

"      "    Zinc     "     "  " 

Potash  "     Green  Precipitate. 

Ammonia  "     Azure-Blue  Color. 

Infusion  of  Nut- Gall  gives,  Brown  Precipitate. 

TESTS  FOR  ANTIMONY  IN  SOLUTION  WITH  FOUR  PARTS 
OF  MURIATIC  ACID  AND  ONE  PART  OF  NITRIC 
ACID. 

Pure  Water  gives White  Precipitate. 

6a 


12  QUARTZ    OPERATOR'S 

Plate  of  Iron  gives Black  Powder  of  the  Metal. 

TESTS   FOR  MERCURY  IN   SOLUTION  WITH   NITRIC  OR 

MURIATIC   ACID. 
Plate  of  Copper  gives ....   Metallic  Mercury. 

"      "  Iron  "     ....    Dark  Powder. 

Gallic  Acid  "     . . .  ,   Orange  Yellow. 

TESTS  FOR  IRON  IN  SOLUTION  WITH  MURIATIC  ACID. 
Infusion  of  Nut- Gall  gives,  Black  Precipitate. 
Ferro-Prusiate   of  Potash 

gives Blue  " 

Ammonia  gives Brownish  Red  Precipitate. 


EXPLANATION    OF   CHEMICAL   TERMS. 
Aqua  Regia. — A  fuming   liquid  composed  of   nitric 
acid  and  muriatic  acid,  viz :     One  part  of  the  former 
and  two  of  the  latter.     This  mixture  readily  dissolves 
gold  and  platinum. 

Sulphate  of  Iron     )  c  Green  vitrioL 

Proto- Sulphate  of  Iron  .  .  )       rr       ■ 

Sulphate  of  Copper Blue    \  itriol,  Blue- Stone, 

Blue  Copperas. 
Nitrate  of  Potassa  .......   Nitre,  Saltpetre. 

Sulphate  of  Soda Glauber  Salts. 

Chloride  of  Sodium Sea  Salt,   Common  Table 

Salt. 

Nitric  Acid Aquafortis. 

Sulphuric  Acid  (Concen-)  0il    f  yitriol 

trated)  j 

Hgdrochloric  Acid Muriatic  Acid. 


HAND    BOOK.  13 

Oxalic  Acid. — Sorrel  Acid. — It  is  commonly  manu- 
factured by  the  action  of  nitric  acid  upon  saccharine  and 
farinaceous  substances. 

Gallic  Acid. — An  acid  obtained  from  nut-galls  or  oak- 
apples.  It  is  also  obtained  from  several  other  vegetable 
astringents. 

Nut-  Galls. — Oak  apples,  which  are  excrescences  pro- 
duced by  small  insects  depositing  their  eggs  in  the 
tender  shoots  of  a  species  of  oak. 

Potassa. — Pure  Potash,  when  refined  by  heat,  is 
called  pearlash.     It  is  a  vegetable  fixed  alkali. 

Aqua-  Vitae. — A  liquid  much  used  for  precipitating 
hombres,  properly  called  aquamortis,  alcohol. 

Chloride  of  Ammonium. — Sal-Ammoniac. 

Catechu. — A  dry,  brown  astringent  extract  obtained 
by  decoction  and  evaporation  from  the  acacia  catechu  in 
India.  It  contains  a  large  portion  of  tannin  or  tannic 
acid. 


ASSAY. 

Assays  are  three  kinds — Mechanical,  dry  and  humid. 

I.  Mechanical  Assays  consist  in  washing  or  otherwise 
freeing,  without  the  aid  of  chemical  agents,  the  metallic 
substances  from  sands  and  other  impurities.  "  Panning 
out"  or  separating  the  gangue  (earthy  matter)  from  the 
metallic  substances,  by  washing  in  common  mining  pans, 
also,  "  winnowing"  as  practiced  on  rich,  dry  sands,  are 
familiar  examples  of  mechanical  assays,  and  require  no 
explanations ;  the  former  of  which  often  furnishes  safer 


14  QUARTZ    OPERATOR'S 

and  more  practical  data  for  extensive  operations,  espe- 
cially in  gold  mining,  than  either  the  dry  or  humid  way. 
II.  The  Dry  way  of  assaying  ores,  usually  requires 
fluxes  for  separating  the  gangue  (earthy  matters)  from 
the  metallic  substances. 

Assay  of  Galena. — Fuse  in  an  earthen  crucible,  at  a 
bright  red  heat. 

Powdered  ore 6  parts. 

Black  Flux, 9       " 

Iron,  in  small  pieces, 2       " 

Extract  from  the  slag,  and  weigh  the  button  of  lead 
thus  obtained. 

Assay  of  Iron. — Fuse  in  a  covered  crucible,  about 
one  hour,  a  well  triturated  mixture  of 

Powdered  and  roasted  ore, 2  parts 

Fluor  Spar, 1       " 

Charcoal,: 1       " 

Common  Salt, » 4       " 

Extract  and  weigh  the  button  of  cast  iron  thus  ob- 
tained. 

Various  other  fluxes,  as  lime,  clay,  etc.,  may  be  em- 
ployed instead  of  the  above.  No  general  formulae  can 
be  given,  as  their  application  depend  upon  the  nature 
of  the  ore. 

Assay  of  Copper  Ores,  containing  no  other  metals 
besides  iron  and  copper : 

Heat  gradually,  at  first,  in  an  earthen  crucible,  and 
afterward  increase  the  heat  to  bright  red,  which  continue 
fifteen  minutes. 


HAND  BOOK.  15 

Powdered  Ore, 1  part. 

Black  Flux, 3     " 

Extract  from  the  slag,  and  weigh  the  button  of  cop- 
per thus  obtained. 

Assay  of  Copper  Ores  containing  sulphur,  but  other- 
wise similar  to  the  above : 

Fuse  in  an  earthen  crucible,  at  a  dull  red  heat,  equal 
parts  of  the  powdered  ore  and  dried  borax.  Extract 
from  the  slag  the  matte  (crude  copper)  button,  which 
pulverize ;  roast  slowly  in  an  earthen  crucible,  and  stir, 
in  the  meantime  with  a  steel  rod,  till  sulphurous  acid 
ceases  to  be  evolved ;  then  increase  the  temperature  to 
a  white  heat,  which  continue  for  several  minutes.  Next 
mix  in  the  same  crucible  : 

The  Roasted  Matte, 1  part 

Black  Flux,  from ...      3  to  4     " 

Cover  the  mixture  with  a  layer  of  fused  borax,  and 
subject  it  to  a  cherry  heat  for  twenty  minutes,  in  a  wind 
furnace ;  then  extract  and  weigh  the  button  of  copper. 

Assay  of  Copper  Ores  containing  arsenic  and  various 
other  metals : 

Obtain  and  pulverize  the  matte  as  in  the  preceding 
case,  then  roast  with  it  powdered  charcoal,  till  the  gar- 
lic odors  of  arsenic  cease  to  be  exhaled. 

Reduce  the  matte  thus  obtained,  as  in  the  last  case, 
with  black  flux  and  borax. 

Cupel  the  button  in  a»  bone-ash  cupel,  with  pure  lead. 
Throw  a  little  borax  glass  over  the  globule  when  its 
rotation  ceases  and  brightening  occurs ;  cool  and  weigh 
the  button  of  copper. 


16  QUARTZ    OPERATOR^ 

ASSAY  OF  GOLD  OR  SILVER,  OR  GOLD  AND  SILVER  ORES 

Fuse  in  an  earthen  crucible : 

Powdered  Ore, 4  parts. 

Litharge, 4       " 

Black  Flux, 3       " 

If  the  ores  contain  much  oxyd  of  lead,  add  only 
black  flux. 

If  the  ores  are  very  rich  in  pyrites,  add  litharge  and 
nitre. 

If  the  button  obtained  be  an  alloy — for  instance,  of 
gold,  silver,  copper  and  lead — make  additions  to  it  of 
silver  and  lead,  so  that  the  prepared  alloy  shall  contain 
as  near  as  may  be,  of 

Gold, 1  part. 

Silver, 3     " 

Lead,   16     " 

First  fuse  the  lead  in  a  bone-ash  cupel,  within  a  muf- 
fle ;  then  add  the  gold  and  silver  inclosed  in  a  piece  of 
paper,  and  continue  the  heat  till  the  button  brightens 
and  becomes  tranquil.  Cool  and  weigh  the  button.  To 
separate  the  gold  from  the  silver,  called  "  parting  of 
gold,"  anneal,  beat  the  button  into  a  thin  plate,  make  it 
into  a  roll,  which  is  termed  a  cornet.  First  heat  this 
plate  or  cornet  in  dilute  nitric  acid  as  long  as  the  acid 
acts  upon  it,  then  in  concentrated  nitric  acid  till  all  of 
the  silver  is  dissolved.  Thoroughly  wash,  dry  and  ignite 
the  cornet.  The  weight  of  silver  is  equal  to  the  weight 
of  the  button  before  "  parting,"  less  that  of  the  refined 
cornet. 


HAND  BOOK.  17 

HUMID  WAY  OF  ASSAY — ASSAY  OF  GALENA. 

1. — Digest  the  powdered  ore  in  equal  parts  of  nitric 
acid  and  pure  water. 

2. — Filter  and  digest  the  residual  several  hours  with 
a  strong  solution  of  carbonate  of  soda. 

3. — Filter  and  digest  the  second  residual  in  dilute 
nitric  acid,  and  again  filter. 

4. — Add  either  a  solution  of  the  sulphate  of  soda,  or 
sulphuric  acid  to  the  collected  filtrates,  as  long  as  any 
precipitate  takes  place. 

5. — Filter,  then  wash  and  dry  the  residual. 

6. — Reduce  the  residual,  with  powdered  charcoal,  in 
an  earthen  crucible ;  cool  and  weigh  the  button. 
ASSAY   OF    COPPER   ORES. 

1. — Digest  the  powdered  ore  in  dilute  nitro-muriatic 
acid. 

2. — Filter  the  solution. 

3. — Add  ammonia  in  excess  to  the  filtrate. 

4. — Filter  and  wash  residual  in  ammonia. 

5. — Evaporate  the  filtrate  to  dryness. 

6. — Dissolve  the  dried  filtrate  in  muriatic  acid. 

7. — Add  clean  iron  or  zinc  plates  to  the  solution  much 
diluted. 

8. — Wash  dry  and  weigh  the  copper  precipitate. 
ASSAY   OF   SILYER  [ORES.* 

1. — Digest  the  pulverized  ore  in  nitric  acid. 

*  Chloride  of  Silver,^  as  found  native,  is  called  horn-silver ;  it  is 
completely  insoluble  in  nitric    acid.    It  is  readily  dissolved  by 


18  QUARTZ    OPERATOR'S 

2. — Add  muriatic  acid  or  solution  of  common  salt  to 
the  silver  solution  as  long  as  any  precipitate  takes 
place. 

3. — Filter  and  dry  the  residual. 

4. — Reduce  the  dry  residual  with  carbonate  of  soda, 
or  black  rosin  in  an  earthen  crucible,  then  cool  and 
weigh  the  button  of  silver.  It  also  may  be  reduced 
with  chalk  and  charcoal. 

ASSAY   OF   GOLD    ORES. 

1. — Digest  the  pulverized  ores  in  one  part  of  nitric 
acid,  and  four  parts  hydrochloric  acid. 

2. — Dilute,  filter  and  evaporate  the  filtrate  to  dry- 
ness. 

3. — Digest  the  dried  filtrate  in  pure  water,  then  boil 
the  solution  with  a  solution  of  sulphate  of  iron,  which 
precipitates  the  gold  as  a  dark-purple  powder. 

4. — Filter  and  heat  the  residual  with  hydrochloric 
acid. 


ammonia,  and  can  be  precipitated  from  this  solution  by  the  ad- 
dition of  nitric  acid.  It  is  also  soluble  in  a  strong,  hot  solution 
of  common  salt,  (see  Augustin  process)  from  which  it  may  be 
precipitated  in  its  metallic  state  by  a  clean  plate  of  copper. 

Quicksilver  partially  decomposes  the  chloride  of  silver  forming 
a  silver  amalgam;  this  is  attended,  however,  with  a  loss  of 
quicksilver,  and  should  be  avoided  in  practical  operations. 
Silver  may  be  revived  from  its  chloride  state  by  being  kept  from 
twelve  to  twenty -four  hours  in  contact  with  clean  iron,  copper  or 
zinc  plates. 

Bromide  of  Silver,  in  almost  every  respect,  resembles  chloride 
of  silver ;  it  is,  however,  less  soluble  in  ammonia. 

Iodide  of  Silver,  found  also  native,  is  readily  converted  into 
chloride  of  silver  by  muriatic  acid,  and  then  may  be  treated  as 
above  described. 


HAND    BOOK.  19 

5. — Filter,  wash,  dry  and  weigh  the  gold  powder. 
Oxalic  acid  substituted  for  the  sulphate  of  iron  pre- 
cipitates the  gold  in  large  flakes. 

ASSAY    OR    ANALYSIS    OF    IRON     ORES    CONTAINING 

MANGANESE. 

1. — Digest  the  roasted  and  pulverized  ore  in  dilute 
hydrochloric  acid. 

2. — Filter,  wash  residual  and  add  washings  to  the 
filtrate. 

3. — Add  muriate  of  barytes  until  no  farther  precipi- 
tation takes  place. 

4. — Filter,  wash  and  add  washings  to  the  filtrate. 

5. — Evaporate  the  filtrate  nearly  to  dryness  and  to  it 
add  sufficient  nitric  acid  to  transform  the  sulphate  of 
iron  to  per-oxyd. 

6. — Add  solution  of  caustic  ammonia  in  excess  to  the 
solution. 

7. — Filter  and  reduce  the  iron  to  the  magnetic  state 
by  heating  the  residual  with  resin  in  an  iron  crucible — 
then  cool  and  weigh. 

8. — Precipitate  the  oxyd  of  manganese  from  the 
filtrate,  by  expelling  the  excess  of  ammonia  with  heat. 

When  the  ores  contain  much  alumina  or  silex,  flux 
them  with  three  or  four  times  their  weight  of  caustic 
potash,  then  digest  in  hydrochloric  acid  and  proceed  as 
above. 


20  QUARTZ    OPERATOR'S 

ASSAY   OR    ANALYSIS    OF    ORES    CONTAINING    GOLD 
SILVER,    COPPER,    LEAD,  IRON   AND    SULPHUR. 

1. — Digest  well  the  pulverized  ore  in  nitric  acid. 

2. — Filter,  wash  residual  (1)  and  add  washings  to 
filtrate  (1). 

3. — Add  to  filtrate  (1)  hydro-chloric  acid,  or  a  solu- 
tion of  common  salt,  which  precipitates  the  silver  as  a 
chloride. 

4. — Filter,  and  digest  residual  (2)  in  hydro-chloric 
acid. 

5. — Filter,  wash  residual  (3)  in  warm  water,  and  to 
filtrate  (3)  with  the  washings  add  filtrate  (2). 

6. — Reduce  the  chloride  of  silver  with  carbonate  of 
soda  by  fusion,  and  weigh  the  button  of  silver. 

7. — Add  to  filtrate  (3),  sulphate  of  soda-in  solution, 
which  precipitates  the  lead  as  a  sulphate. 

8. — Filter,  and  add  the  residual  to  residual  (1). 

9. — Evaporate  filtrate  (4)  to  any  desirable  extent. 

10. — Add,  in  excess,  to  concentrated  filtrate  (4)  am- 
monia, which  precipitates  sesqui-oxyd  of  iron. 

11. — Filter,  wash  residual  and  add  washings  to 
filtrate  (5). 

12. — Dry  and  heat  the  residual  in  hydrogen  gas 
within  a  glass  tube  as  long  as  any  vapor  of  water  is  dis- 
engaged, then  weigh  the  iron.  This  powder,  with  glass 
as  a  flux  at  a  high  heat,  becomes  a    button  of  iron. 

13. — Treat  filtrate  (5),  after  evaporating  it  to  dryness 
with  hydro-chloric  acid,  then  add  clean   iron  or  zinc 


HAND    BOOK.  21 

plates  to  the  solution  diluted.  Wash,  dry  and  weigh  the 
copper  precipitate. 

14. — Treat  residual  (1),  first  with  a  strong  solution 
of  carbonate  of  soda,  then  with  dilute  nitric  acid  ;  and  to 
the  combined  filtrates  add  -sulphuric  acid,  or  a  solution 
of  the  sulphate  of  soda.  Wash,  dry  and  reduce  the  pre- 
cipitate with  powered  charcoal  in  an  earthen  crucible ; 
then  cool  and  weigh  the  button  of  lead. 

15. — Digest  the  last  residual  in  nitro-muriatic  acid ; 
add  chloride  of  sodium  in  solution,  filter,  precipitate  the 
gold  from  its  solution  by  the  addition  of  sulphate  of  iron 
in  solution ;  wash,  dry  and  weigh  the  gold. 

16. — If  the  gold  may  be  alloyed  with  silver  and 
copper,  precipitate  the  copper  from  the  last  filtrate  by 
the  addition  of  iron  or  zinc  plates ;  wash,  dry  and  add 
the  weight  of  the  precipitate  to  the  copper  already 
obtained. 

Heat  the  residuary  ore  in  a  strong  solution  of 
chloride  of  sodium,  filter  and  precipitate  the  silver  with 
a  clean  copper  plate ;  wash,  ignite  and  add  the  silver  to 
that  already  obtained. 

17. — Burn  off  the  sulphur  and  weigh  residuary  ore. 
The  sum  of  the  weights  of  the  gold,  silver,  copper,  lead, 
iron  and  calcined  ore  taken  from  the  weight  of  the 
original  ore,  leaves  the  weight  of  the  sulphur. 

EECIPES. 
Mack  Mux. — Black  Flux  is  prepared  by  introducing 
gradually  in  small  quantities,  into  a  crucible  heated  to  a 


22  QUARTZ    OPERATOR'S 

very  dull  redness,  a  mixture  of  either  two  parts  of  cream 
of  tartar  and  one  of  nitre ;  or  equal  parte  of  cream  of 
tartar  and  nitre.  White  Flux  is  similarly  prepared  ex- 
cept that  the  mixture  consists  of  one  part  of  cream  of 
tartar  and  two  parts  of  nitre. 

Iron  Rust  Cement. — To  one  hundred  parts  of  pow- 
dered and  sifted  iron  borings,  add  one  part  of  sal-am- 
moniac. Moisten  the  mixture  with  water  to  a  pasty  con- 
sistency for  use. 

Lead  Cement — Red  or  white  lead  in  oil,  four  parts  ; 
iron  borings,  two  to  three  parts.  Makes  a  good  cement 
for  steam  boilers,  steam  pipes,  etc. 

Solders,  for  Lead. — Melt  one  part  of  block  tin,  and 
when  in  a  state  of  fusion  add  two  parts  of  lead.  Resin 
should  be  used  with  this  solder. 

For  Tin. — Pewter  four  parts,  tin  one  part,  and  bis- 
muth one  part ;  melt  them  together.  Resin  is  also  used 
with  this  solder. 

For  Iron. — Tough  brass  with  a  small  quantity  of 
borax. 

For  Iron,  Copper  and  Brass. — Spelter,  that  is  an  alloy 
of  zinc  and  copper  in  nearly  equal  parts,  is  used. 

Quicksilvering  of  Copper  Plate. — First  thoroughly 
cleanse  the  surface  of  the  plate,  and  rub  it  over 
with  quicksilver,  or  with  the  nitrate  of  mercury. — 
The  surface  is  sometimes  cleansed  by  simply  scouring 
it  with  wood  ashes,  brick  dust,  or  fine  sand ;  and  some- 
times by  washing  it  with  dilute  acid  or  strong  alkali. 
When  acid  is  employed,  its  corrosive  qualities  should 


HAND   BOOK.  23 

be  neutralized  before  the  application  of  the  quicksilver. 
Nitrate  of  mercury,  when  crystalized,  is  readily  con- 
verted to  a  liquid  by  heat,  in  which  state  it  may  be  ap- 
plied as  a  wash  to  the  plate. 

ROASTING. 

Boasting  is  employed  to  dissipate  the  volatile  parts 
of  ore  by  heat,  and  is  effected  in  heaps  or  furnaces. 

In  Heaps. — Alternate  layers  of  fuel  and  ore,  usually 
as  it  comes  from  the  mine,  are  heaped  up  to  the  depth  of 
several  feet.  The  lowest  or  ground  layer  is  of  wood, 
arranged  by  cross-piling  so  as  to  afford  a  free  circulation 
of  air.     The  upper  layers  may  be  of  wood  or  coal. 

The  ratio  of  fuel  in  volume  to  that  of  ore  varies  from 
1  to  6  to  1  to  18.  Fine  ores  and  those  rich  in 
sulphur  require  less  than  coarse  ores  and  poor  in  sul- 
phur. The  fire  is  kindled  through  vertical  openings  or 
chimnies  which  extend  to  the  ground  layer.  These 
openings  are  closed  when  the  fuel  has  well  taken  fire. 
The  roasting  should  be  slow  and  uniform  in  all  parts  of 
the  heap.  The  heat  may  be  regulated  by  opening  or 
closing  the  draft  holes  and  chimnies.  Several  days  and 
even  months,  sometimes,  are  required  for  roasting  one 
heap.  Ores  similarly  piled  with  fuel  are  sometimes 
roasted  in  walled  inclosures  provided  with  side  openings. 

Furnaces, — There  are  a  great  variety  of  furnaces. 
Those  mostly  approved  for  the  roasting  of  ores  embrac- 
ing also  calcining  and  chloridvzing  are  the  reverberatory. 
The  interior  walls  of  the  furnace  should  be  of  the  best 
fire  brick  laid  edgewise  ;  the  outer  walls  may  be  of  com- 


24  QUARTZ    OPERATOR'S 

mon  building  brick  or  stone.  The  furnace  must  be  well 
tied  with  iron  rods,  and  carefully  dried  before  being 
used. 

The  Reverbreatory  Furnace  is  constructed  sometimes 
with  one  and  sometimes  with  two  hearths  or  soles  one 
above  the  other.  In  the  double  hearth  furnace,  for  in- 
stance, in  the  treatment  of  silver  ores  the  roasting  and 
sulphatization  are  effected  on  the  upper  sole,  and  the 
calcining  and  chloridizing  on  the  lower.  The  ore  pul- 
verized fine,  is  charged  upon  the  upper  sole  to  the  depth 
of  from  two  to  four  inches,  and  is  kept  well  stirred  du- 
ring the  roasting.  The  heat  should  be  at  a  low  temper- 
ature, not  exceeding  brown  or  dull  red.  The  access  of 
air  should  be  free.  A  small  jet  of  steam  into  the  fur- 
nace assists  in  regulating  the  temperature  and  also  fa- 
cilitates oxydation.  The  addition  of  powdered  charcoal 
in  small  quantities  may  be  made  to  advantage  when  the 
ores  contain  arsenic.  If  the  ores  are  poor  in  sulphur  add 
from  two  to  three  per  cent,  of  the  sulphate  of  iron.  The 
first  operation  of  roasting  and  sulphatizing  is  accom- 
plished in  four  or  five  hours.  Then  through  an  opening 
in  the  upper  hearth  the  ore  is  let  fall  upon  the  lower, 
where  it  is  heated  for  some  time  at  a  temperature  not 
much  higher  than  that  above.  The  heat  is  then  gradu- 
ally increased  to  cherry  red,  at  which  it  is  kept  during 
the  time  required  for  calcining  and  chloridizing.  The 
heat  should  never  exceed  bright  red.  The  ore  is  fre- 
quently stirred.  When  calcination  is  complete  a  mix- 
ture of  common  salt  melted  and  pulverized  and  seven 


HAND    BOOK.  25 

parts  of  cold  calcined  ore  are  added  to  the  hot  ore,  esti- 
mated at  fifteen  parts,  and  quickly  and  thoroughly  mixed 
with  it  by  stirring.  Calcination  is  usually  effected  in  four 
or  five  hours,  and  chlorination  in  fifteen  or  twenty 
minutes. 

PURIFICATION   OF   MERCURY. 

Mercury  for  the  purposes  of  amalgamation  should  be 
pure.  Any  foreign  substance  such  as  lead,  tin,  zinc,  or 
bismuth  diminishes  its  properties  of  combining  with 
gold  and  silver.  To  free  from  these  and  other  impuri- 
ties, 

1st.  Distil  the  impure  mercury.  A  retort  for  this 
process  may  readily  be  made  of  a  common  quicksilver 
flask  and  iron  pipe  of  syphon  form.  The  short  leg  of 
the  pipe,  a  few  inches  long,  is  attached  to  the  flask  i  n 
the  place  of  the  removed  stopper. 

The  long  leg,  three  or  four  feet  in  length,  inclines 
downward  from  the  bend.  The  retort  should  not  be 
jver  two  thirds  filled  with  mercury.  The  heat  ought 
first  to  be  applied  to  the  short  leg  of  the  pipe  and  upper 
part  of  the  retort,  then  to  all  parts  of  the  flask  alike. 
The  long  leg  of  the  pipe  must  be  kept  cold.  This  may 
be  effected  by  wrapping  it  with  cloths  and  pouring  on 
cold  water.  The  discharge  end  may  also  be  immersed 
in  cold  water,  kept  in  the  receiver.  The  heat  should  be 
uniform,  and  the  distillation  slow.  The  common  covered 
retort  is  far  preferable  to  the  one  described. 

2.  Heat  and  frequently  agitate  the  distilled  mercury 
in  thin  sheets,  with  one  part  of  nitric  acid  and  two  parts 


26  QUARTZ    OPERATOR'S 

of  pure  water.  The  heat  should  be  kept  at  120  degrees 
Fahrenheit,  for  several  hours.  Repeat  these  operations 
until  satisfactory  results  are  obtained.  Then  pour  off 
the  mercury  for  use. 

3.  Digest  the  crust  (nitrate  of  mercury  and  impuri- 
ties) in  nitric  acid.  Then  dilute  the  solution,  filter,  pre- 
cipitate the  mercury  by  metallic  copper,  and  add  it  to 
the  mercury  already  obtained.  Or  the  nitrate  of  mercu- 
ry may  be  converted  to  a  liquid,  simply  by  heat,  and 
the  metal  then  precipitated  by  copper  plate. 

EXTRACTION  OF  GOLD  BY  THE  PAN  PROCESS. 

1.  The  rock,  as  it  comes  from  the  mines,  is  usually 
crushed  wet  by  stamps,  to  a  fine  granular  state,  and  run 
into  large  tanks. 

2.  Charges  of  the  reduced  ore,  with  sufficient  water 
to  form  a  thin  paste,  are  thoroughly  ground  in  iron  pans. 
As  gold  found  in  rock  exists  almost  without  exception  in 
a  metalic  state,  friction  alone  is  required  to  fit  it  for 
amalgamation. 

3.  Quicksilver  is  ordinarily  added  to  the  pulp,  as  the 
pans  commence  running.  To  avoid  grinding  the  quick- 
silver excessively,  the  addition  is  sometimes  made  with 
the  muller  slightly  raised,  after  the  reduction  of  the  ores 

4.  The  charge  is  then  drawn  off  and  washed,  leaving 
the  amalgam  in  the  separators. 

5.  The  proportions  usually  observed,  for  instance,  in 
the  Wheeler  &  Randall  grinders  and  amalgamators,  are 

Ore  to  the  charge, 1,200  pounds. 

Quicksilver  to  the  charge  of  ore, ....      75         " 


HAND    BOOK.  27 

Revolutions  of  muller, 60  to  75 

Time  of  reducing, 2  to  3  hours. 

As  gold-bearing  rock  is  seldom  found  sufficiently  rich 
to  render  it  advisable  to  treat  the  entire  mass  in  pans, 
the  above  method  is  subject  to  various  modifications,  of 
which  the  following  are  a  few : 

1.  The  heavier  and  richer  portions  of  the  rock,  as 
crushed,  are  concentrated  by  revolving-blankets,  buddies 
or  other  machinery,  and  then  pulverized  and  amalga- 
mated in  pans. 

2.  Amalgamation  is  commenced  in  the  batteries 
during  the  crushing  operation,  and  is  carried  on  through 
a  series  of  shaking  tables,  riffles,  and  copper  plates.  The 
richer  portions  of  the  tailings  are  then  concentrated  and 
treated  in  pans. 

3.  Grinding  and  amalgamating  are  effected  in  pans 
while  the  reduced  ores  are  flowing  continuously  through 
them. 

4.  The  sulphurets  or  concentrated  tailings  are  some- 
times roasted  in  a  reverberating  furnace,  before  being 
ground  and  amalgamated. 

5.  Thin  layers  of  the  concentrated  sulphurets  or  tail- 
ings are  spread  in  inclosures  open  to  the  sky,  and 
allowed  to  remain  a  long  time,  for  instance,  a  year.  The 
tailings  are  occasionally  turned  with  shovels  and  the 
lumps  broken,  so  as  to  expose  as  much  surface  as  possi- 
ble to  the  action  of  the  air.  Common  salt  mixed  with 
the  tailings    assists  in  their   oxydation.       When    quite 


28  QUARTZ    OPERATOR'S 

thoroughly  oxydized,  they  are  treated  in  pans.  This 
is  very  economical  and  effectual,  and  by  it  the  yield  of 
gold,  (especially  if  very  fine)  to  the  ton  is  frequently 
much  greater  than  was  obtained  at  first  from  the  same 
ores. 

EXTRACTION  OF  GOLD  BY  CHLORINATION. 

1.  Pulverized  Ores,  containing  gold,  having  been  well 
roasted,  cooled  and  moistened  with  water,  are  put  into 
closely  covered  wooden  cisterns,  whose  bottoms  are  so 
constructed  that  chlorine  gas  can  permeate  the  mass 
from  underneath. 

2.  Chlorine  gas  produced  by  heating  sulphuric  acid, 
per  oxyd  of  manganese  and  common  salt,  in  a  suitable 
generator,  is  caused  to  enter  the  cisterns  at  the  bottom? 
through  leaden  pipes.  The  effect  of  the  chlorine  on  the 
gold,  is  to  produce  terchloride  of  gold. 

3.  Pure  water,  after  the  chloride  has  done  its  duty> 
which  takes  from  ten  to  fifteen  hours,  the  covers  being 
removed,  is  added  sufficient  to  keep  the  cisterns  even 
with  the  mass.  The  effect  of  the  water  is  to  dissolve 
the  terchloride  of  gold.  The  solution  is  then  drawn  off 
into  glass  vessels. 

4.  Sulphate  of  iron,  in  solution,  is  used  to  precipitate 
the  gold,  which  may  then  be  gathered  as  a  powder. 

EXTRACTION  OF  SILVER  BY  THE  PATIO  PROCESS. 

1.  Patio  signifies  a  yard.  For  amalgamating  pur- 
poses, the  floor  of  the  yard  is  made  level,  paved  with 
brick  or  granite  blocks,  surrounded  by  high  walls,  and 


HAND    BOOK.  29 

usually  left  open  to  the  sky.  On  this  floor  circular 
batches  of  silver  ore,  reduced  to  an  inpalpable  paste  by 
stamps  and  arastras,  or  other  machinery,  are  spread  to 
the  depth  of  seven  to  twelve  inches,  and  inclosed  by  low 
close  curbs. 

2.  Salt,  varying  in  quantity  according  to  its  quality 
and  the  richness  of  the  ore,  is  well  mixed  with  the  pulp 
by  treading  it  with  horses,  mules,  or  oxen,  and  turning 
it  with  shovels.  The  effect  of  the  salt  is  to  desulphur- 
ize the  sulphurets,  and  produce  chloride  of  silver.  The 
batch  is  then  left  one  entire  day. 

3.  Magistral,  that  is,  roasted  and  pulverized  copper 
pyrites,  varying  in  quantity  with  its  quality,  the  richness 
of  the  ores  and  season,  is  well  mixed  with  the  pulp  after 
it  has  been  subjected  to  the  treading  and  turning  opera- 
tion one  hour.  The  ultimate  effect  of  the  magistral  is 
to  revive  the  silver  by  depriving  it  of  its  chlorine. 

4.  Quicksilver  is  added,  usually  in  three  charges  to 
the  mass,  by  being  sprinkled  in  minute  particles  through 
cloth  or  other  porous  substance.  After  the  addition  of 
the  first  charge  of  quicksilver,  the  batch  is  thoroughly 
mixed,  thrown  into  heaps  of  about  one  ton  each,  smooth- 
ed and  left  at  rest  one  whole  day.  The  treading,  turn- 
ing and  heaping  operation  is  performed  every  other  day, 
occupying  five  or  six  hours,  and  is  found  much  more 
effective  in  a  morning  than  an  evening.  The  second 
charge  of  quicksilver  is  added  and  similarly  treated 
when  it  is  ascertained  by  washing  a  small  quantity  of 
the  mixture,  that  the  first  has  been  well  incorporated. 

b3 


30  QUARTZ    OPERATOR'S 

After  the  second  charge  has  performed  its  work,  the 
third  charge  is  added  to  take  up  any  stray  particles  of 
silver,  and  to  fit  the  amalgam  better  for  separation. 

5.  Lime  is  added  to  cool,  and  magistral  to  heat  the 
mass,  according  as  it  may  be  too  hot  or  too  cold.  Too 
much  heat  is  indicated  by  the  quicksilver  becoming  ex- 
tremely divided,  and  of  a  dark  color,  with  occasional 
brown  spots  upon  its  surface.  Too  little  heat  is  indica- 
ted by  the  quicksilver  retaining  its  natural  color  and 
fluidity.  A  proper  degree  of  heat  is  indicated  by  the 
amalgam's  being  of  a  greyish-white  color,  and  yielding 
readily  to  a  slight  pressure. 

6.  The  proportions  to  the  ton  of  ore,  valued  at  fifty 
dollars,  are : 

Sea  Salt,  of  good  quality, ,  . . .  .  80  pounds. 

Magistral. — When  containing  ten  per  cent., 
of  the  sulphate  of  copper, 

in  summer, 20  " 

in  winter, 10  " 

Quicksilver — First  charge, ...    14  " 

Second  charge, 5  " 

Third  charge, 7  " 

Lime. — More  or  less,  see  section  5th,.  .  .15  " 

An  excess  of  magistral,  quicksilver,  or  lime  is  inju- 
rious. An  excess  of  salt  causes  a  loss  of  quicksilver 
but  is  not  otherwise  injurious. 

The  time  employed  in  treating  a  batch  of  ore  varies 
from  twelve  to  sixty  days.  Light  and  good  weather 
greatly  facilitate  operations. 

7.  The  separation  is  accomplished  by  agitating  the 


HAND    BOOK.  31 

pulp  or  mixture   with  abundance  of  water,  in  a  large, 
deep,  circular  vessel,  and  causing  the  lighter  portions  of 
the  mass  to  flow  slowly  off,  until  the  amalgam  is  gath- 
ered by  itself. 
EXTRACTION  OF  SILVER  BY  THE  FREYBERG  PROCESS. 

1.  This  process  takes  its  name  from  Freyberg,  a 
place  in  Germany,  where  it  was  first  practiced.  The 
ores,  if  possible,  are  assorted  so  as  to  contain  not  less 
than  twenty-five  per  cent,  of  sulphurets.  When  they 
contain  less,  the  sulphate  of  iron  is  added  to  make  up  the 
deficiency.  When  more,  then  a  sufficient  quantity  of 
the  richest  in  sulphurets  is  roasted  without  sea-salt  to 
make  good  the  ratio :  the  ores  are  crushed  dry. 

2.  Sea-Salt  and  crushed  ores  are  thoroughly  mixed 
together,  roasted  in  a  reverberatory  furnace,  and  then  re- 
duced to  an  impalpable  powder  in  a  suitable  mill.  The 
salt  and  heat  transform  the  sulphurets  of  silver  to 
chloride  of  silver. 

3.  Wrought  Iron,  in  small  pieces,  with  a  pasty  mixt- 
ure of  the  reduced  ores  and  water  are  put  into  German 
barrels,  which,  making  twenty  revolutions  a  minute,  are 
run  two  hours.  The  effect  of  the  iron  is  to  revive  the 
silver  to  its  metallic  state. 

4.  Quicksilver  is  then  poured  into  the  barrels,  after 
which  they  are  run  sixteen  hours  continuously,  except 
the  time  taken  to  regulate  the  consistency  of  the  pulp, 
by  the  addition  of  ore  or  water.  At  the  end  of  the  time 
run,  the  casks  are  filled  with  water  and  revolved  quite 

b4 


32  QUARTZ    OPERATOR'S 

slowly  for  one  or  two  hours,  when  the  mass  is  dis- 
charged into  lai  ge  vats  and  the  amalgam  separated  by 
washing. 

5.  The  Proportions  to  the  ton  of  ore  valued  at  $75.00 
per  ton,  are 

Sea-Salt,  added  before  the  roasting  process,  200  lbs. 

Wrought  Iron,  added  to  the  ton  of  roasted 
ore 200  " 

Quicksilver,  added    to  the  ton  of  roasted 
ore.. 1000  " 

EXTRACTION  OF  SILVER  BY  THE  VEATCH  PROCESS. 
The  only  essential  difference  between  this  and  the 
Freyberg  process  consists  in  the  employment  of  tubs 
instead  of  barrels,  and  the  use  of  steam  directly  in  the 
pulp.  Vertical  plates  of  iron  or  copper,  for  reviving  the 
silver  from  its  chloride  state,  are  fastened  to  the  muller 
arms,  so  as  to  revolve  edgewise  through  the  pulp  or 
mass.  The  operations  are  greatly  hastened  by  the 
application  of  steam,  so  that  not  more  than  five  or  six 
hours  are  required  for  the  treatment  of  a  charge  of  ore. 

EXTRACTION  OF  SILVER  BY  THE  PAN  PROCESS. 

1.  The  Ores,  as  they  come  from  the  mines,  are 
usually  crushed  wet  to  a  granular  state  by  stamps,  and 
run  into  a  series  of  large  settling  tanks.  To  crush  wet, 
and  at  the  same  time  fine,  is  very  objectionable,  as 
much  silver  thereby  is  carried  off  by  the  water. 

2.  Charges  of  the  reduced  ores,  with  sufficient  water 
to  form  a  soft,  pasty  mass,  are  put  into  iron  pans  con- 


HAND    BOOK.  33 

structed  as  grinders,  which  are  run  from  two  to  six 
hours,  according  to  their  reducing  properties.  Water  is 
occasionally  added  during  the  grinding  process,  as  the 
condition  of  the  pulp  may  require. 

3.  Quicksilver  is  ordinarily  poured  into  the  pans  as 
they  commence  running.  Sometimes,  to  avoid  grinding 
it  excessively,  the  muller  is  slightly  raised  and  the  ad- 
dition made  after  the  reduction  of  the  ores. 

4.  Chemicals,  differing  in  kind  and  proportions,  to 
almost  an  indefinite  extent  are  employed.  As  to  their 
practical  value,  a  diversity  of  opinion  prevails  among 
the  most  experienced  and  intelligent  amalgamators 
and  mill-men.  In  pans  of  slow  motion  and  of  little 
grinding  capacity,  certain  chemicals,  in  the  treatment  of 
some  ores,  have  been  used  to  advantage.  Their  em- 
ployment and  proportions,  in  all  cases,  depend  upon  the 
composition  and  character  of  the  ores.  Experience 
thus  far,  chiefly  goes  to  show  that  the  chemicals  in  pans, 
which  grind  rapidly,  are  not  only  valueless  but  in  many 
instances  injurious  to  amalgamation.  In  pans  of  this 
character,  the  sulphurets  of  silver  ores  become  not  only 
mechanically  divided,  but  chemically  decomposed.  The 
heat  of  the  steam  contributes  to  the  attainment  of  this 
desirable  object ;  the  iron  of  the  pans  serves  also  to 
revive  any  silver  existing  as  a  chloride. 

The  proportions  usually  observed  in  operating  the 
Wheeler  &  Randall  grinders  and  amalgamators,  are : 

5b 


34  QUARTZ    OPERATOR'S 

Ore  to  the  charge, 1,200  lbs 

Quicksilver  to  the  charge  of  ore  valued 

at  $50  per  ton, 200     " 

Revolutions  of  muller  per  minute, 60  to  75 

Heat,  to  nearly  the  boiling  point  of  water. 

Time  of  working  charge, , 2  to  3  hs. 

The  charge  is  next  drawn  off  and  separated  by  wash- 
ing. The  grinders  and  amalgamators  should  be  well 
cleansed  before  being  recharged. 

6.  A  few  of  the  chemical  recipes  employed  in  Nevada, 
to  the  ton  of  ore,  valued  at  $50  : 
recipe  I. 

Sulphuric  Acid, 3  pounds. 

Sulphate  of  Copper, 2         " 

Common  Salt, 15         " 

rec.  ii. 

Sulphuric  Acid, 2         " 

Alum, 2 

Sulphate  of  Copper 1.5      " 

REC.  III. 

Sulphate  of  Copper, 1.2  " 

Sulphate  of  Iron, 1.0  " 

Sal  Ammoniac, 0.8  " 

Common  Salt, 2.0  " 

REC.  IY. 

Catechu, 2         " 

Sulphate  of  Copper, 2         " 

Common  Salt, 25         " 


HAND    BOOK.  35 

REC  V. 

Sulphate  of  Iron, 1.5      " 

Nitric  Acid, 1.5      " 

Common  Salt, 15.0       " 

KEC.  VI. 

Muriatic  Acid, 30  ounces. 

Peroxyd  of  Manganese, ...  8      " 

Sulphate  of  Copper, 10      " 

Sulphate  of  Iron, 10      " 

The  salt  is  applied  half  an  hour  before  the  other 
chemicals. 

SEPARATION  OF  SILVER  FROM  LEAD  BY  THE  PATTIN 
SON  PROCESS. 

1.  This  process  is  founded  on  these  facts:  If  a 
melted  alloy  of  silver  and  lead  is  stirred  while  cooling 
slowly,  crystals  of  lead  form  and  sink,  which  may  be 
removed  with  a  drainer.  A  large  portion  of  the  lead 
may  thus  be  separated  from  the  silver. 

2.  Cast-iron  pans,  capable  of  holding  about  five  tons 
each,  and  provided  with  fire  places,  are  arranged  in  a 
series,  as  A,  B,  C,  D,  E,  F,  G,  in  a  straight  line. 

3.  The  metal  of  ores  containing  silver  and  lead  as  it 
comes  from  ordinary  smelting  works,  is  melted,  for  in- 
stance, in  pan  D,  and  then  allowed  to  cool  very  slowly. 
The  metal  while  cooling  is  stirred,  especially  near  the 
edges  of  the  pan,  with  an  iron  bar.  As  soon  as  crystals 
form  and  sink  to  the  bottom,  they  are  taken  out  with  an 
iron  drainer  raised  to  a  temperature  somewhat  higher 

b6 


36  QUARTZ    OPERATOR'S 

than  that  of  the  metal  bath.  From  one  half  to  two 
thirds  of  the  charge  is  thus  removed  to  pan  E,  and  the 
balance  taken  to  pan  C.  Other  charges  of  D,  are  simi- 
larly treated  and  disposed  of.  The  charges  of  C  and  E 
are  treated  and  disposed  of  in  like  manner,  except  that 
the  crystals  of  E  go  to  F,  and  the  balance  to  D,  and  the 
crystals  of  C  go  to  D,  and  the  balance  to  B.  Thus,  after 
successive  meltings  and  drainings,  the  alloys  rich  in 
silver  pass  to  A,  while  the  lead,  almost  entirely  de- 
prived of  silver,  goes  to  G.  The  alloys  obtained  in  pan 
A  are  then  subjected  to  cupellation.  An  alloy  contain- 
ing over  six  hundred  dollars  of  silver  to  the  ton  should 
not  be  treated  by  this  process. 

SEPARATION  OF  SILVER  FROM  COPPER  BY  THE  LIQUA- 
TION PROCESS. 

1.  This  process  is  founded  on  these  facts :  Lead  and 
copper  fused  together  form  an  alloy,  which,  if  rapidly 
cooled,  maintains  an  intimate  admixture,  but  if  slowly 
cooled,  separates.  An  alloy  of  lead  and  copper  slowly 
heated  to  near  its  point  of  fusion,  also  separates.  Silver, 
if  contained  in  the  alloy,  goes  with  the  lead. 

2.  Either  an  alloy  of  copper  or  silver,  or  matte  (crude 
black  copper  reduced,  but  not  refined  from  sulphur  and 
other  impurities),  containing  silver,  as  it  comes  from  the 
smelting  furnace,  is  melted  with  lead  of  about  four 
times  its  weight,  in  a  cupola  furnace,  and  cast  into  plain 
circular  plates  which  are  suddenly  cooled.  These  plates, 
called  "  liquation  cakes,"  are  arranged  on  their  edges, 


HAND    BOOK.  37 

with  alternate  layers  of  charcoal,  in  a  liquation  furnace. 
The  charcoal  is  then  ignited,  and  a  degree  of  heat  pro- 
duced somewhat  below  that  of  the  fusing  point  of  cop- 
per. The  lead  and  silver  melt  and  flow  into  a  receiver, 
while  the  copper,  in  a  porous  state,  retains  the  forms  of 
the  original  cakes.  If  the  separation  may  have  been 
imperfect,  the  cakes  are  farther  treated  by  being  raised 
to  a  higher  degree  of  heat  in  the  "  sweating  furnace." 
The  silver  is  then  separated  from  the  lead  by  cupella- 
tion. 

SEPARATION    OF    SILVER  FROM  LEAD   BY  THE  PARKE 
PROCESS. 

1.  Lead,  containing  silver,  is  fused  in  large  cast-iron 
pots.  Melted  zinc  is  added  and  well  stirred  in  the  alloy. 
The  fire  being  withdrawn  from  under  the  pot,  the  whole 
is  left  at  rest  for  a  short  time. 

2.  The  silver  and  zinc  separating  from  the  lead,  form 
an  independent  alloy,  which  is  skimmed  from  the  sur- 
face of  the  metal  bath,  as  long  as  it  rises. 

3.  This  scum  alloy,  containing  some  lead,  is  heated  in 
a  liquation  retort.  The  silver  and  lead  fuse,  and,  to  a 
great  extent,  flow  into  prepared  moulds.  The  alloy  thus 
run  off  is  then  cupelled;  the  alloy  of  zinc  and  silver 
remaining  in  the  retort,  are  partially  separated  by  dis- 
tillation. The  silver  thus  obtained  is  freed  of  its  im- 
purities by  cupellation. 

4.  The  proportions  are : 


38  QUARTZ    OPERATOR'S 

Charge  of  argentiferous  lead  to  the  pot 

usually  from 6  to  7  tons. 

Charge  of  zinc  to  the   ounce,  of  silver 

by  estimation, 1.5  to  2  pounds 

Quantity  of  silver  to  the  ton  of  lead.  .  10  to  15  ounces 
Time  of  stirring  alloy,  after  the  addition 

of  zinc,  from 10  to  15  hours. 

The  alloy  prepared  for  cupellation  contains,  of  silver, 
to  the  ton,  about  1,000  ounces. 

SEPARATION     OF    SILVER     FROM     LEAD     BY     CUPEL- 
LATION. 

1.  The  Alloy  of  silver  and  lead  is  melted  in  a  circular 
reverberatory  furnace  provided  with  openings  through  its 
sides  for  the  admission  of  metal,  heat,  currents  of  air, 
and  for  the  escape  of  vapors  or  litharge.  The  escape  is 
opposite  the  blast  opening.  The  roof  or  top  of  the  fur- 
nace is  of  dome-form  and  movable.  At  each  cupella- 
tion, the  hearth,  usually  of  hollow  form,  is  broken  up 
and  replaced  by  one  made  of  clay,  sand  and  carbonate 
of  lime. 

2.  Blasts,  or  currents  of  air,  are  blown  continually 
during  the  operation  upon  the  surface  of  the  fused  alloy, 
promoting  oxydation  of  the  lead  and  causing  the  litharge 
to  pass  out  through  the  escape  opening.  The  gate-way 
of  this  opening  is  kept  level  wTith  the  surface  of  the 
metal  within.  The  silver  thus  separated  from  the  lead 
remains  on  the  hearth  of  the  furnace  in  nearly  a  pure 
state.  It  is  deprived  of  what  lead  it  may  contain  by 
the  humid  way  of  assay. 


HAND    BOOK.  30 

EXTRACTION  OF  SILVER  BY  THE   AUGUSTIN   PROCESS. 

1.  This  Process,  employed  thus  far  chiefly  in  the 
treatment  of  matte,  (impure  copper)  containing  silver,  is 
founded  on  the  solubility  of  chloride  of  silver  in  a  hot, 
concentrated  solution  of  common  salt. 

2.  The  Matte,  as  it  comes  from  the  cupola  or  high 
furnace,  is  crushed  dry  by  stamps,  pulverized  in  suit- 
able mills  and  bolted.  The  coarser  portions  thus 
obtained  are  taken  to  the  copper  works. 

3.  The  Roasting  of  the  powdered  matte  in  a  reverber- 
atory  furnace  is  commenced  at  a  low  temperature  with 
a  free  access  of  air.  By  careful,  uniform  roasting,  at  a 
dull  red  heat,  the  sulphurets  of  silver,  iron  and  copper 
are  produced.  The  heat  is  then  increased  to  cherry-red 
which  decomposes  the  sulphates  of  iron  and  copper,  but 
not  the  sulphate  of  silver. 

4.  Salt,  previously  melted,  pulverized  and  mixed 
with  cold  calcined  matte,  is  added  to  the  hot  matte  in 
the  furnace  and  thoroughly  mixed  with  it  by  stirring. 
The  sulphate  of  silver  is  thus  transformed  to  chloride  of 
silver. 

5.  The  Apparatus  for  the  humid  operations  consist  of 
a  large  heating  reservoir,  a  series  of  dissolving  tubs,  two 
large  settling  cisterns,  four  precipitating  tubs  to  each  one 
of  the  dissolving  tubs,  and  two  large  receptacles, 
arranged  in  the  order  here  given  on  descending  steps. 
The  dissolving  and  precipitating  tubs  are  nearly  cylin- 
drical.    They  are  provided  with  filters  made  of  small 


40  QUARTZ    OPERATOR'S 

sticks  and  straw,  covered  with  cloth ;  a  vertical  parti- 
tion, resting  on  the  filter,  divides  each  tub  into  two 
unequal  compartments. 

6.  The  Ghloridized  Matte  being  put  into  the  larger 
compartments  of  the  dissolving  tubs,  sufficient  of  the  hot 
salt  solution  from  the  heating  reservoir  above  to  com- 
pletely immerse  the  matte,  is  let  into  the  tubs ;  they  are 
then  left  at  rest  one  hour.  The  discharge  cocks  of  the 
heating  reservoir  and  tubs  then  being  opened,  the  hot 
salt  solution  is  filtered  through  the  contents  of  the  tubs, 
and  run  off  from  the  smaller  compartments,  at  openings 
at  first  above  the  level  of  the  matte,  afterwards  at  open- 
ings near  the  bottoms  of  the  tubs,  into  the  settling 
cisterns,  until  a  test  with  clean  copper  plate  shows  no 
trace  of  silver  in  the  filtered  solution. 

7.  Copper  (copper  cement)  is  put  into  each  of  the 
upper  two  precipitating  tubs  in  the  several  series  of 
four,  and  iron  (wrought  scrap  iron)  into  each  of  the 
lower  two.  The  chloride  solution  from  the  settling 
cisterns  is  then  slowly  filtered  through  the  several  series 
of  precipitating  tubs,  and  the  filtered  solution  run  into 
the  large  receptacles  below.  The  silver  is  precipitated 
by  the  copper  in  the  upper  tubs,  and  the  copper  in  solu- 
tion is  precipitated  by  the  iron  in  the  lower  tubs.  The 
silver  is  taken  twice  a  week  from  the  precipitating  tubs 
and  refined.  The  copper  precipitated  in  the  lower  tubs 
is  transferred  to  the  upper  tubs.  The  filtered  matte  is 
washed  and  taken  to  the  copper  works.     The  filtered 


HAND    BOOK.  41 

solution,  in  the  receptacles,  is  pumped  into  the  heating 
reservoir  and  used  again. 

8.   The  Proportions  usually  observed  are : 

Matte,  before  roasting,  should  con- 
tain of  sulphur,  not  less  than,  20  per  ct. 

Charge  of  Matte,  to  the  furnace, 

for  roasting  and  calcining,.  .  500  pounds. 

Charge.— Melted   Salt, 35         " 

Roasted  Matte, 220         " 

Add  same  for  chloridizing. 

Time. — Roasting  on  the  upper  sole 

of  Furnace 4  to  4J  hs. 

Calcining   on  lower    sole   of 

Furnace 4  to  4£  " 

From 8  to  9      " 

Time  of  chloridizing,  from 15  to  20  minutes. 

Charge  of  chloridized  matte  to  the 

tub,  from 1000  to  1200  lbs. 

Salt — In  the  solution,  in  reference 

to  the  water,  from 20  to  25  per  ct. 

Degrees  of  Heat  of  salt  solution.  .  131°  Fahr. 

Time  of  dissolving  and  precipita- 
ting, from  ...      20  to  24  hours. 

Solution  of  Sahy  run  through  each 
tub  to  1000  pounds  of  matte, 
from     200  to  250  cubic  ft. 

Depth  of  Copper  in  precipitating 

tubs,  about 6  inches. 

Depth    of  Iron   in    precipitating 

tubs,  about ...    6       " 


42  QUARTZ    OPERATOR'S 

EXTRACTION  OF  SILVER  BY  THE  ZIERVOGEL  PORCESS. 

1.  This  Process,  employed  thus  far  chiefly  in  the 
treatment  of  matte  (impure  copper)  containing  silver, 
is  founded  on  the  solubility  of  sulphate  of  silver  in  hot 
water. 

2.  The  Matte,  as  in  the  Augustin  process,  having 
been  thoroughly  pulverized,  is  carefully  roasted  and 
calcined  till  the  sulphates  of  iron  and  copper  are  com- 
pletely decomposed,  but  none  of  the  sulphate  of  silver. 
When  small  quantities  of  the  roasted  matte,  thrown  hot 
into  water,  give  only  a  very  slight  blue  color,  the  cal- 
cination is  regarded  complete. 

3.  The  Sulphatized  Matte  is  then  treated,  in  all  respects, 
the  same  as  the  chloridized  matte,  (see  sec.  6,  page  JJ^) 
in  the  Augustin  process,  except  that  pure  water  is  em- 
ployed instead  of  solution  of  salt. 

4.  The  Proportions  usually  observed  are  : 
Matte,  before  roasting,  should  con- 
tain of  sulphur,  not  less  than,  20  per  ct. 

Charge  of  Matte  to  the  Furnace, .  500  lbs. 

Time. — Roasting  on  upper  sole  of 

Furnace, « 4  to  4J  hours. 

Calcining   on    lower   sole  of 

Furnace, . .    .............       4  to  4£  hours. 

From 8  to  9     " 

Charge   of  sulphatized    matte  to 

the  tub,  from 1000  to  1200  lbs. 

Degrees  of  Heal  of  the  water  for 


HAND    BOOK.  43 

dissolving 149°  Fahr. 

Time  of  dissolving  and  precipita- 
ting, from 20  to  24  hours. 

Hot  Water  run  through   each  tub, 

from 200  to  250  cubic  ft. 

Depth  of  Copper  in  upper  precipi- 
tating tubs, 6  inches. 

Depth  of  Iron  in  lower  precipita- 
ting tubs, «       " 

EXTRACTION  OP  SILVER  BY  THE  PATERA  PROCESS. 

1.  In  this  Process  the  ores  are  thoroughly  pulverized 
and  chloridized  by  roasting  with  common  salt. 

2.  Hot  Water  to  dissolve  the  chlorides  of  various  base 
metals  is  filtered  through  the  chloridized  ores  put  in 
tubs  similar  to  the  dissolving  tubs  in  the  Augustin  pro- 
cess. The  ores  are  then  cooled  and  transferred  to 
similar,  but  smaller  tubs. 

3.  Hyposulphite  of  Soda,  in  cold  solution,  is  then 
filtered  through  the  ores  and  run  into  precipitating  tubs 
until  all  the  chloride  of  silver  is  completely  dissolved. 

4.  Poly  sulphide  of  Sodium,  sufficient  to  produce  a 
neutral  liquor,  is  then  added,  which  precipitates  the 
silver  as  a  sulphide  in  sacks  fitted  to  the  inside  of  the 
tubs.  This  neutral  liquor  is  preserved  for  lixiviating 
purposes. 

5.  The  Sulphide  of  Silver  thus  obtained,  after  being 
washed  in  warm  water,  pressed  and  dried,  is  heated 
under  muffles  with  free  access  of  air  till   nearly  all  the 


44  QUARTZ    OPERATOR'S 

sulphur   is    expelled.     The  metallic  silver  is  then  re- 
refined. 


MECHANICS. 

Force. — That  which  produces  or  tends  to  produce  mo- 
tion, or  change  of  motion,  is  termed  force. 

Work. — The  product  of  force  and  the  distance  through 
which  it  is  exerted,  is  termed  icork — mechanical  work. 

Units. — The  units  of  force,  distance,  and  time  are  re- 
spectively one  (1)  pound,  one  (1)  foot,  and  one  (1) 
minute. 

Horse  Power. — Thirty  three  thousand  (33,000)  units 
of  work  constitute  one  (1)  "  horse  power,"  that  is,  thirty- 
three  thousand  pounds  raised  vertically  one  (1)  foot  in 
one  (1)  minute,  or  its  equivalent. 

TO  FIND  THE  HORSES'  POWER  IN  A  GIVEN  TIME. 

Rule. — Divide  the  product  of  the  weight  in  pounds 
and  the  vertical  distance  in  feet  through  which  the 
weight  is  to  be  raised,  by  the  product  of  the  time  in 
minutes  and  thirty-three  thousand.  (33,000.) 

Ex.  1. — Required  the  horses'  power  necessary  to  drive 
forty-five  (45)  stamps,  each  stamp  weighing  six  hundred 
and  forty  (640)  pounds,  falling  ten  inches,  and  making 
seventy-seven  (77)  drops  per  minute,  allowing  twenty- 
five  per  cent,  for  friction. 

Cat     45X640X77X10--12=1848000. 

1848000X1.25=2310000. 

2310000h-33000=70  horses'  power.    Ans. 

Ex.  2. — How  many  horses'  power  are  required   to 


HAND    BOOK.  45 

raise  water  three  hundred  (300)  feet  by  a  single  acting 
pump  seven  (7)  inches  diameter,  thirty  (30)  inches 
stroke,  making  fifteen  (15)  lifting  strokes  per  minute, 
allowing  thirty -five  (35)  per  cent,  for  friction  ? 

Gal.     15  X  30— 450  inches,  column  of  water  raised. 

450-=- 12=37.5  feet,  column  of  water  raised. 

7X7X,7854-f-144=,2672  area  of  end  of  column  of 
water. 

,2672X37.5=10.02  solid  inches  in  column  of  water. 

10.02X62.  5=626.25  pounds  in  column  of  water. 

626.25X1.35=845.4375  pounds  with  friction  added. 

845.4375  X  300-^-330000=7.68  horses*  power.    Ans. 

Ex,  B. — The  slant  depth  of  the  hoisting  shaft  of  the 
Eureka  Mine,  Sutter  Creek,  is  one  thousand  (1000) 
feet ;  the  dip  of  the  lode  being  sixty  (60°)  degrees ;  how 
many  horses'  power  are  required  to  raise  one  ton  (2,000 
pounds)  of  rock  to  the  surface  in  five  minutes,  allowing 
fifty  per  cent,  for  friction  ? 

90°— 60°=30°  complement. 

1000^-2=500  feet  side  of  right  angled   triangle  op- 
posite 30°  1000X1000=100000;  500X500=250000; 
1000000—250000=750000. 
"l/750000=:866.0254  perpendicular  depth  of  mine. 

866.0254X1.50=1299.0376,  with  friction  added. 

1299.0376X2000=2598075  ;  33000X5=165000. 

2598085-^-165000=15.75  horses'  power.     Ans. 

Remarks. — 1.  It  is  found  by  experience  that  it  re- 
quires to  reduce  by  stamps  hard  quartz  rock  (frequently 


46  QUARTZ    OPERATOR'S 

called  by  miners,  live  rock,)  from  the  size  usually  fed 
into  batteries  to  the  ordinary  granular  size  coming  from 
the  same,  about  one  horse  power  to  the  ton  in  twenty- 
four  hours  ;  and  to  farther  reduce  it  from  the  granular 
state  by  the  common  pan-grinders  and  amalgamators  to 
a  "  slum "  or  slime  of  economical  fineness,  about  one 
horse  power  in  the  same  length  of  time. 

2.  That  the  Wheeler  &  Randall  Grinder  and  Amal- 
gamator, four  feet  diameter,  making  sixty-five  revolu- 
tions per  minute,  will  reduce  from  the  granular  to  the 
slime  condition,  five  tons  of  rock  per  twenty-four  hours. 

Note. — It  is  estimated  by  those  using  the  Wheeler  and 
Randall  Grinder  and  Amalgamator,  that  it  requires  to 
run  each  four  foot  machine  sixty-five  revolutions  per 
minute,  three  (3)  horse  power.  This  is  somewhat  less 
than  the  inventors  were  ready  to  believe,  on  account  of 
the  extraordinary  reducing  properties  of  their  invention. 

3.  That  it  requires  to  run  a  Separator  seven  feet  di- 
ameter, (not  grinding,)  about  one  half  of  one  horse 
power. 

VARIED  MOTION. 
Laws  of  Uniformly  Varied  Motion. — 1.  In  uniformly 
varied  motion,  the  path  described  at  the  end  of  any  time 
is  half  that  which  the  body  would  describe  in  the  same 
time  if  it  were  to  move  uniformly  with  the  velocity  ac- 
quired during  this  time. 

2.  In  uniformly  accelerated  motion,  the  paths  de- 
scribed at  the  end  of  any  two  times,  are  to  each  other  as 
the  squares  of  these  times. 

3.  That  these  paths  are  to  each  other  as   the  square 


HAND    BOOK.  47 

of  the  velocities  acquired  at  the  end  of  the  correspond- 
ing times. 

Let  one  second  be  a  unit  of  time  ;  then  will  the  times 
of  a  falling  body,  in  vacuo,  be 

1,  2,  3,  4,  5,  6,  7,  8,  9,  etc.,  etc. 

The  corresponding  fall  during  each  second,  will  be 

1,  3,  5,  7,  9,  11,  13,  15,  17,  etc.,  etc. 

The  fall  during  any  number  of  seconds,  will  be 

1,  4,  9,  16,  25,  36,  49,  64,  81,  etc.,  etc. 

And  the  velocities  acquired  at  the  end  of  each  second, 
will  be 

2,  4,  6,  8,  10,  12,  14,  16,  18,  etc.,  etc. 

Now,  a  body  at  the  equator  falls,  in  vacuo,  as  deter- 
mined by  experiments,  16.0904  feet  in  one  second  of 
time.  The  resistance  of  the  atmosphere  does  not  much 
retard  the  velocity  of  heavy  falling  bodies.  Let  then, 
sixteen  feet  represent  the  distance  which  a  falling  body 
will  describe  in  one  second  of  time,  when  impressed  by 
gravity  alone.  The  velocity  acquired  at  the  end  of 
the  first  second  of  time,  is  called  the  "initial  veloc- 
ity," and  is  found  to  be  32.1808  feet;  that  is,  twice 
16.0904  feet.  This  velocity,  due  to  the  force  of  gravity, 
is  usually  denoted  by  g;  that  is,  g=32.1808,  which, 
for  most  practical  purposes,  may  be  taken  at  32  feet. 
TO  FIND  THE  DISTANCE  A  BODY  WILL  FALL  IN  TERMS 
OF  THE    VELOCITY. 

Rule  1. — Divide  the  square  of  the  velocity  by  sixty- 
four  (64). 


48  QUARTZ    OPERATOR'S 

Example. — The  velocity  is  256  feet,  what  distance 
has  the  body  fallen  ? 

Calculation.  256X256-f-64=1024  feet.    Ans. 
TO  FIND  WHAT  DISTANCE  IN  FEET  A  BODY  WILL  FALL 
IN  A  GIVEN  TIME. 

Rule  2. — Multiply  the  square  of  the  time  in  seconds 
by  si  teen  (16). 

Example. — What  distance  will  a  body  fall  in  one 
minute  ? 

Calculation.  60X60X16=57600  feet.     Ans. 

TO  FIND  THE  VELOCITY  IN  FEET,  IN  TERMS  OF  THE 
TIME. 

Rule  3. — Multiply  the  time  in  seconds  by  thirty-two. 

Example. — What  velocity  does  a  falling  body  acquire 
in  seven  seconds  (7)? 

Calculation.  32X7=224  feet.     Ans. 

TO  FIND  THE  VELOCITY  IN  TERMS  OF  THE  DISTANCE. 

Rule  4. — Multiply  the  square  root  of  the  distance  by 
eight  (8). 

Example. — What  velocity  will  a  body  acquire  by 
falling  one  hundred  and  ninety-six  feet  (196)  ? 

Calculation.  8|/i96=112  feet.     Ans. 
TO   FIND    THE    TIME    FALLEN,  THE    VELOCITY    BEING 
GIVEN. 

Rule  5. — Divide  the  velocity  by  thirty-two  (32). 

Example. — The  velocity  is  1920  feet,  what  time  has 
it  fallen? 

Calculation.  1920-7-32—60  seconds.    Ans. 


HAND    BOOK.  49 

TO   FIND  THE  TIME  A  BODY  HAS    FALLEN,  THE    DIST- 
ANCE BEING  GIVEN. 

Rule  6. — Divide  the  square  root  of  the  distance  fal- 
len by  four  (4). 

Example. — How  long  will  it  take  a  body  to  fall  one 
hundred  and  forty-four  feet  (144)  ? 

Calculation,     j/ 144 -^-4— 3  seconds.     Ans. 
WATER    POWER. 

The  theoretical  velocity  with  which  a  liquid  issues 
from  an  orifice  in  the  bottom  or  side  of  a  vessel  that  is 
kept  full,  is  equal  to  that  which  a  heavy  body  would 
acquire  by  falling  from  the  level  of  the  surface  to  the 
level  of  the  orifice.  The  rules,  therefore,  under  the 
head  of  "  Varied  Motion,"  apply  equally  well  to  falling 
bodies  and  to  hydraulics. 

The  practical  velocity  estimated  for  the  entire  open- 
ing, is  considerably  less  than  the  theoretical  velocity 
owing  to  oblique  currents  and  to  friction.  These  oblique 
currents  produce  a  contraction  in  the  vein  or  stream. 
The  minimum  transverse  section  of  the  contracted  vein, 
is  the  plane  at  which  the  velocity  is  nearly  equal  to  the 
theoretical  velocity.  The  quantity  of  water  which  will 
be  discharged  in  a  certain  time,  depends  upon  the  form 
of  the  opening,  as  well  as  upon  the  head.  Tlius,  by 
means  of  a  conical  tube  of  the  form  of  the  contracted 
vein,  the  velocity  at  the  opening  or  smaller  end  of  the 
tube,  is  nearly  equal  to  the  theoretical  velocity.  The 
theoretical  velocity  per  second  (rule  4,  varied  motion), 


50  QUARTZ    OPERATOR'S 

is  eight  times  the  square  root  of  the  head  in  feet.  The 
actual  velocity  estimated  for  the  entire  opening,  as  ordi- 
narily constructed,  is  five  and  four-tenths  the  square 
root  of  the  head. 

Water,  as  a  power  or  force,  is  exerted  on  water 
wheels  by  its  weight  and  by  its  impulse.  Weight  and 
impulse  are  combined  on  the  overshot  and  breast  wheels. 
The  theoretical  work  accomplished  by  weight  is  the 
product  of  its  force  and  the  vertical  distance  through 
which  it  is  exerted.  The  theoretical  work  accomplished 
by  impulse,  is  the  product  of  the  force  produced  by 
weight  of  the  flow  of  water,  and  the  vertical  height  or 
head  necessary  to  produce  the  velocity  with  which  the 
weight  moves. 

The  available  work  depends  not  only  upon  the  mag- 
nitude of  the  force  exerted,  but  upon  the  direction  of 
that  force  in  reference  to  the  direction  given  to  the  re- 
sistance ;  also  upon  the  form  of  the  floats  or  buckets  of 
the  wheel,  friction,  losses  by  leakage,  etc. 

The  average  efficiency  of  various  water  wheels,  run- 
ning under  favorable  circumstances,  as  found  by  expe- 
rieuce,  is  as  follows,  to  wit : 

Undershot,  having  flat,  radial  floats 33 

Poncelet,  improved  undershot, , 60 

Turbine,  for  example,  the  "  Jouval," 68 

Reaction,  for  example,  the  Scotch  Turbine, ....  66 
Overshot  and  Breast,  the  efficiency  of  that  part 
of  the  fall  acting  by  weight,  is  about 78 


HAND    BOOK.  51 

And  of  that  part  acting  by  impulse, 40 

The  best  velocities  of  the  various  water  wheels, 
as   compared  with  the  supply  velocities,  are 
as  follows : 
Undershot  and  Low  Breast,  at  circumference, .  .  50 

Turbines,  at  the  middle  of  ring  of  buckets, 65 

Reaction,  at  circumference, 97 

Overshot,  at  circumference, .50 

The  velocity  of  the  overshot  wheel  at  its  circumfer- 
ence, should  be  about  six  feet ;  which  is  due  a  head  of 
2.25  feet. 

Let  the  vertical  distance  from  the  centre  of  the  open- 
ing in  the  gate,  to  the  surface  of  the  water  in  the  flume 
or  reservoir,  be  termed  the  head,  and  the  vertical  dis- 
tance from  the  centre  of  the  opening  in  the  gate  to  the 
lower  edge  of  the  wheel,  the  fall 


2c 


52 


QUARTZ    OPERATOR'S 


TABLE    OF     COEFFICIENTS      FOR      ESTIMATING     THE 
HORSES'  POWER  OF   WATER  WHEELS. 


Head. 

Head. 

Head. 

Head. 

ft.  in. 

coefficient. 

ft.  in. 

coefficient 

ft.  in 

coefficient. 

ft.  in 

coefficient. 

r 

12 

1    7 

54" 

3  2 

76" 

9. 

128 

2 

17 

1    8 

55 

3  4 

78 

10. 

135 

3 

21 

1    9 

56 

3  6 

80 

12. 

148 

4 

25 

1.10 

58 

3  8 

82 

14. 

160 

5 

28 

1.11 

59 

3  10 

84 

16. 

171 

6 

30 

2    0 

60 

4  0 

85 

20. 

191 

7 

33 

2    1 

62 

4  3 

88 

25. 

213 

8 

35 

2    2 

63 

4  6 

90 

30. 

233 

9 

37 

2    3 

64 

4  9 

93 

36. 

256 

10 

39 

2    4 

65 

5  0 

95 

49. 

298 

11 

41 

2    5 

66 

5  4 

98 

64. 

341 

1  0 

43 

2    6 

67 

5  8 

101 

81- 

384 

1    1 

44 

2    7 

69 

6  0 

104 

100. 

426 

1   2 

46 

2    8 

70 

6  6 

109 

121. 

469 

1   3 

48 

2    9 

71 

7  0 

113 

144. 

511 

1   4 

49 

2.10 

72 

7  6 

1174 

169. 

554 

1  5 

51 

2.11 

73 

8  0 

121 

196. 

597 

1   6 

52 

3    0 

74 

8  6 

124 

225. 

639 

TO  FIND  THE  HORSES7  POWER  FOR  VARIOUS  WATER 
WHEELS. 

Rule, — Multiply  the  product  of  the  tabular  coefficient 
opposite  the  given  head,  the  area  of  the  opening  in  the 
gate  in  square  inches,  the  entire  head  in  feet  (head  and 
fall  in  case  of  overshot  and  breast  wheels),  by  the  effi- 
ciency of  the  class  of  wheel,  pointing  off  six  figures  as 
decimals. 

Example  1. — The  dimensions  of  a  stream  are  two 
inches   by   two   hundred   inches.     What  is  its  horses' 


HAND    BOOK.  53 

power,  applied  to  a  breast  wheel  affording  a  fall  of  ten 
feet? 

Calculation.  2  inches  by  200  inches=400  square 
inches  opening. 

Tabular  coefficient  opposite  2  feet  3  inches, ....  64 

Efficiency  of  wheel,  arising  from  impulse 40 

Efficiency  of  wheel  arising  from  weight, 78 

Head,  2  feet  3  inches  =2.25 

2.25X40=90,  product  of  efficiency  and  head. 

lOX'8—780  product  of  efficiency  and  fall. 

90+780=870  sum  of  products. 

870X400X64=22.27  horses'  power.     Ans. 

Example  2. — The  dimensions  of  the  stream  are  ten 
inches  square,  the  head  twenty-five  feet,  what  is  its 
horses'  power  applied  to  a  good  turbine  ? 

Calculation.     10X10=100  square  inches  opening. 

Tabular  coefficient  opposite  head  of  twenty-five 

feet, =213 

Efficiency  of  turbine  =68. 
'100X213X68X25=36.21  horses'  power.     Ans. 

STEAM  POWER. 
Steam,  as  a  force,  acts  by  elastic  pressure.  The  law 
"  that  in  compressing  the  same  quantity  of  air,  or  of  a 
-  perfect  gas  into  smaller  spaces,  the  volumes  occupied  by 
it  are  inversely  proportioned  to  the  pressures,"  does  not 
hold  good  in  relation  to  saturated  steam.  In  the  follow- 
ing table,  P  denotes  the  total  pressure  in  pounds  per 
square  inch ;  T  the  corresponding  temperature,  and  V 

3c 


54 


QUARTZ    OPERATOR  S 


the  volume  of  the  steam  compared  to  the  volume  of  the 
water  that  has  produced  it. 

TABLE  OF  PRESSURES,  TEMPERATURES  AND  VOLUMES. 


p- 

T. 

1 

i02.r 

5 

162.3 

10 

193.3 

14.7 

212.0 

15 

213.1 

20 

228.0 

25 

240.1 

30 

250.4 

35 

259.3 

40 

267.3 

45 

274.4 

50 

281.0 

V. 

P. 

T- 

20582 

60 

292.7^ 

3813 

65 

298.0 

2358 

70 

302  9 

1642 

75 

307.5 

1610 

80 

312.0 

1229 

90 

320.2 

996 

100 

327  9 

838 

110 

334.6 

726 

120 

341.1 

640 

135 

350.1 

572 

150 

358.3 

518 

165 

366.0 

V. 

P. 

T. 

437 

180 

372.9 

405 

190 

377.5 

378 

200 

381.7 

353 

210 

386.0 

333 

220 

389,9 

298 

230 

393.8 

270 

240 

397.5 

247 

250 

401.1 

227 

260 

404.5 

203 

270 

407.9 

184 

280 

411.2 

169 

300 

417.5 

V. 


155 
148 
141 
135 
129 
123 
119 
114 
110 
106 
102 
96 


HAND    BOOK. 


55 


TABLE     FOR    ESTIMATING 
STEAM  FOR   A  GIVEN 


THE    MEAN   PRESSURE    OF 
CUT-OFF    OF   STROKE. 


TJNJACKETED 

CYLINDER. 

JACKETED   CYLINDER. 

cut-cff 

coefficient,    correction. 

cut-off. 

coefficient. 

correction. 

A 

.177 

12.098 

A 

.186 

11.966 

A 

.244 

11.113 

A 

.254 

10.966 

A 

.303 

10.246 

A' 

.314 

10.084 

i 

.356 

9.467 

i 

.370 

9.261 

A 

.407 

8.717 

A 

.417 

8.570 

i 

.496 

7.409 

i 

.505 

7.297 

i 

.572 

6.290 

i 

.582 

6.145 

A 

.639 

5.307 

A 

.648 

5.174 

A 

.697 

4.454 

A 

.707 

4.307 

t 

.748 

3.704 

1 

.756 

3.587 

A 

.797 

2.984 

A 

.800 

2.940 

T 

.833 

2.455 

T 
2 

.840 

2.352 

H 

.869 

1.926 

11 

¥0 

.874 

1.852 

9 

3" 

.894 

1.558 

I 

.900 

1.470 

It 

.923 

1.132 

it 

.929 

1.044 

A 

.945 

0.808 

7 

ITT 

.945 

0.808 

1 

.960 

0.588 

3 

4 

.960 

0.588 

t 

.976 

0.353 

t 

.976 

0.353 

ft 

.986 

0.206 

H 

.986 

0.206 

A 

•997 

0.044 

A 

.997 

0.044 

c4 


56  QUARTZ    OPERATOR'S 

By  the  table  of  pressures,  temperature  and  volumes,  it 
will  be  seen  that  the  volume  of  steam  under  a  pressure 
of  thirty  pounds  to  the  square  inch  produced  from  a 
cubic  inch  of  ice-cold  water  is  838  cubic  inches  ;  while 
under  a  pressure  of  ninety  pounds  to  the  square  inch, 
the  volume  is  298  cubic  inches.  Thus  the  ratio  of  the 
two  pressures  is  as  30  to  90,  or  as  1  to  3,  while  the 
inverse  ratio  of  the  respective  volumes  of  steam  is  as  1 
to  2.81.  The  mechanical  effect  deduced  from  the 
above  data  is  as  follows:  838X30-^-12=2095,  and 
298X90—12=2235.  Then  2235—2095=140  differ- 
ence of  mechanical  effects,  and  140-^-2095=,0668 ; 
showing  an  advantage  of  nearly  seven  per  cent,  in 
favor  of  using  steam  at  the  higher  pressure. 

By  the  table  for  estimating  the  mean   pressure  of 
steam  for  a  given  cut-off  of  stroke,  the  coefficients  for 
one-fourth  (J)  cut-off  are  572  in   the  unjacketed.  cylin- 
der, and  582  in  the  jacketed  cylinder. 
Then  582—572=10, 
and  10--572=,0175; 
showing  an  advantage  of  one  and  three-fourths  of  one 
per  cent,  in  favor  of  the  jacketed  cylinder  for  the  given 
cut-off  of  stroke. 

The  back  pressure  of  steam  in  the  cylinder  of  an 
engine  of  ordinary  structure  is  found,  by  experience,  to 
be  about  four  pounds  to  the  square  inch  above  the 
atmospheric  pressure  ;  the  velocity  of  piston  being  three 
hundred  (300)  feet  per  minute.     It  is  also  found  by  ex- 


HAND    BOOK.  57 

perience  that  the  excess  of  the  back  pressure  above  the 
atmospheric  pressure  varies  nearly  as  the  square  of  the 
velocity  of  the  piston. 

Thus,  if  the  velocity  of  the  piston  be  four  hundred 
(400)  feet  per  minute,  the  back  pressure  will  be  7.11 
pounds. 

Calculation.  300X300=90000;  400X400=160000; 
4X160000^-90000=7.11  pounds. 

TO  FIND  THE  MEAN  PRESSURE  OF  STEAM  FOR  A 
GIVEN  CUT-OFF  OF  STROKE. 
Rule. — Multiply  the  excess  of  the  pressure  of  steam 
above  the  atmospheric  pressure  per  square  inch  as  it 
enters  the  cylinder  by  the  tabular  coefficient  opposite 
the  given  cut-off,  pointing  off  three  figures  as  decimals, 
and  deduct  from  the  product  the  tabular  correction  for 
the  same  cut-off. 

Example. — What   is   the   mean   pressure   of   steam 
entering  the  cylinder  at  a  pressure  of  ninety  pounds  to 
the  square  inch,  and  cut-off  at  three- tenths  stroke? 
Calculation. — Tabular  coefficient,  unjacketed 

cylinder,  for, T\  stroke=,639 

Correction  for  same, =5.307 

Then,  ,639X90=57.510 

57.510—5.307=52.203  pounds.     Ans. 
And,  jacketed  cylinder, 

,648X90=58.320 
58.320—5.174=53.146. 

c5 


58  QUARTZ    OPERATOR'S 

TO  FIND  THE   EFFECTIVE   HOKSES;  POWER  OF  A  NON- 
CONDENSING   STEAM   ENGINE. 

Rule. — Multiply  four  times  the  square  of  the  diame- 
ter of  the  piston  in  inches  by  the  product  of  the  number 
of  revolutions,  length  of  stroke  in  feet,  and  the  differ- 
ence between  the  average  forward  pressure  and  the 
back  pressure  of  steam  in  pounds  per  square  inch? 
pointing  off  five  figures  as  decimals. 

Example. — What  is  the  effective  horses'  power  of  an 
engine,  the  diameter  of  the  piston  being  sixteen  inches) 
the  length  of  stroke  three  feet,  the  number  of  revolu- 
tions fifty  per  minute,  and  the  average  forward  pressure, 
above  the  atmospheric  pressure,  seventy-five  pounds  per 
square  inch? 

Gal. — The  back  pressure  =4  pounds. 
75—4=71  pounds. 

Then, 

16X16X4X50X3X71=109.05  horses' power.  Ans. 

Ex.  2. — What  is  the  effective  horses'  power  of  an 
engine,  the  diameter  of  the  piston  being  twelve  inches, 
the  length  of  stroke  two  feet,  the  pressure  of  steam,  as 
it  enters  the  cylinder,  sixty  pounds  in  excess  of  atmos- 
pheric pressure,  cut-off  at  one-half  stroke,  and  making 
seventy-five  revolutions  per  minute? 

Gal. — Back  pressure  4  pounds. 

Tabular  coefficient  for  J  stroke=,833. 
"       correction  for  same  =2.455. 

833x60—2.455—4=43.525  effective  pressure. 


HAND    BOOK.  59 

Then,    12X12X4X43.525X2X75=37.60    horses' 
power.     Ans. 


MECHANICAL    POWERS. 

There  are  three  classes  of  mechanical  powers,  viz  : — 
the  lever,  pulley  and  inclined  plane. 

The  wheel  and  axle  belong  to  the  first  class,  and  are 
sometimes  termed  the  perpetual  lever. 

The  wedge  and  screw  belong  to  the  third  class. 

Weight  signifies  the  resistance  to  be  overcome,  and 
power  the  force  which  overcomes  or  tends  to  overcome 
the  resistance. 

THE    LEVER. 

The  arms  of  a  lever  are  the  portions  of  it  which  are 
intercepted  between  the  power  and  fulcrum,  and  be- 
tween the  weight  and  fulcrum. 

There  are  three  kinds  of  levers,  in  which  : — 

1.  The  fulcrum  is  between  the  power  and  weight. 

2.  The  weight  is  between  the  power  and  fulcrum. 

3.  The  power  is  between  the  fulcrum  and  weight. 
Assuming  the  lever  itself  to  have  no  weight,  and  no 

friction,  the  condition  of  equilibrium  or  balance,  is  as 
follows : 

The  product  of  the  power  and  the  length  of  arm  to 
which  it  is  applied,  is  equal  to  the  product  of  the  weight 
and  the  length  of  arm  to  which  it  is  applied. 

Ex.  1.  If  one  arm  of  a  lever  be  ten  feet,  and  the 

c6 


60  QUARTZ    OPERATOR'S 

other   two  feet,  what    power  must  be  applied    to   the 
longer  arm  to  balance  a  weight  of  1000  pounds? 

Gal.     1000X2-^-10=200  pounds.     Ans. 

Ex,  2.  If  the  radius  of  the  axle,  of  "  the  wheel  and 
axle,"  be  six  inches,  and  the  radius  of  the  wheel  forty- 
eight  inches,  what  power  must  be  applied  to  the  circum- 
ference of  the  wheel  to  balance  2400  pounds  at  the 
circumference  of  the  axle? 

Gal.     2400  X  6^48=300  pounds.     Ans. 
THE  PULLEY. 

Assuming  the  pulley  (as  commonly  arranged)  to  be 
without  weight  and  free  from  friction  and  stiffness  of 
cordage,  the  condition  of  equilibrium  or  balance  is,  that 
the  weight  is  equal  to  the  product  of  the  power  and  the 
number  of  cords  at  the  movable  block. 

Ex. — What  weight  will  be  balanced  by  a  power  of 
one  hundred  pounds,  there  being  three  movable  pulleys, 
or,  in  other  words,  six  cords  at  the  movable  block? 

Gal.     100X6=600  pounds.     Ans. 
THE   INCLINED   PLANE. 

Assuming  that  there  is  no  friction,  and  that  the  direc- 
tion of  the  power  applied  is  parallel  to  the  plane,  the 
conditions  of  equilibrium  of  a  body  sustained  by  any 
force  on  an  inclined  plane,  is  as  follows : 

The  product  of  the  power  and  the  length  of  the  plane 
is  equal  to  the  product  of  the  weight  and  the  height  of 
the  plane. 

Ex. — What  power  would  be  necessary  to  sustain  a 


HAND    BOOK.  61 

rolling  weight  of  1,200  pounds  upon  an  inclined  plane 
of  10  feet  length  and  6  feet  perpendicular  height? 

Gal— 1200X6-^-10=720  pounds.   Ans. 

If  the  power  acts  parallel  to  the  base  of  the  plane, 
then  the  product  of  the  power  and  the  length  of  the 
base  is  equal  to  the  product  of  the  weight  and  the  height 
of  the  plane. 

Ex. — What  power  would  be  necessary  to  sustain  a 
rolling  weight  of  1200  pounds  upon  an  inclined  plane 
whose  base  is  8  feet  and  height  6  feet  ? 

Gal     1200X6^-8=900  pounds.     Ans. 

Ex.  3d. — Omitting  the  consideration  of  friction,  what 
power  applied  to  the  back  of  a  wedge  of  the  form  of 
either  a  single  or  double  inclined  plane,  and  in  the  di- 
rection of  the  base  of  the  inclined  plane,  will  raise  a 
weight  of  2400  pounds,  the  back  of  the  wedge  being  3 
inches  thick,  and  the  base  being  48  inches  long? 

Gal     2400X3-^-48=150  pounds.     Ans. 

Ex.  4. — Omitting  the  consideration  of  friction,  if  the 
threads  of  a  screw  be  2  inches  apart,  and  a  power  of 
500  pounds  be  exerted  at  the  end  of  a  lever  84  inches 
long,  what  weight  or  force  will  be  produced  at  the  end 
of  the  screw  ? 

Gal.     84X2X-2T2-=528  inches,  base  of  inclined  plane. 

Distance  of  threads  apart=2  inches,  height  of  in- 
clined plane,  528X500-^2=132000  pounds.     Ans. 

THIN    CYLINDERS. 
To  determine  the  thickness  of  a  thin  hollow  cylinder ; 


62  QUARTZ    OPERATOR'S 

the  internal  radius,  pressure,  and  the  tenacity  of  the 
material  being  given. 

Rule.  Multiply  the  internal  radius  in  inches  by  the 
fluid  pressure  in  pounds,  and  divide  the  product  by  the 
tenacity  per  square  inch  of  the  material. 

Ex. — The  internal  radius  of  a  cylinder  being  30 
inches,  the  fluid  pressure  250  pounds  to  the  square  inch, 
and  the  tenacity  of  the  material  of  the  cylinder  twelve 
thousand  pounds  per  square  inch,  what  is  the  thickness 
of  the  cylinder  ? 

Cal.     250X30=7500. 

7500^12000=|  inches.     Ans. 
To   determine  the  fluid  pressure,   the   internal  radius, 

thickness  of  cylinder,  and  tenacity  of  material  being 

given. 

Rule. — Divide  the  product  of  the  thickness  of  the 
cylinder  and  tenacity  of  the  material,  by  the  internal 
radius. 

Ex. — The  thickness  of  the  cylinder  being  one-fourth 
of  an  inch,  the  tenacity  eighteen  thousand  pounds.,  and 
the  radius  six  inches,  what  fluid  pressure  will  the  cylin- 
der withstand  per  square  inch  ? 

Gal.  18000X^6=750  pounds.     Ans. 
THICK   HOLLOW    CYLINDERS. 

To  determine  the  thickness  of  thick,  hollow  cylinders, 
the  internal  radius,  the  fluid  pressure  and  the  tenacity 
of  the  material  of  the  cylinder  being  given. 

Rule. — Subtract  one  from  the  square  root  of  the  quo- 


HAND    BOOK.  63 

tient  of  the  sum  and  difference  of  the  tenacity  per 
square  inch  of  the  material  of  the  cylinder,  and  the 
fluid  pressure  per  square  inch,  and  multiply  this  differ- 
ence by  the  internal  radius. 

Ex.  1. — The  internal  radius  of  a  thick,  hollow  cylin- 
der being  nine  inches,  the  tenacity  of  the  material  of 
the  cylinder  ten  thousand  pounds  per  square  inch,  what 
is  the  requisite  thickness  of  the  cylinder  ? 

Cal.  Sum    of  tenacity   and 

fluid  pressure,  10000-^8000=18000 

Difference    of  tenacity   and 

fluid    pressure,  10000—8000=2000 

Quotient  of  sum  and  difference,      18000-^2000=9 

Square  root  of  quotients,  -j/9— 3 

Difference  between  root  and  one,  3 — 1=2 

Product  of  radius  and  this  differ- 
ence 9X2=18  inches.    Ans. 

To  determine  the  fluid  pressure  per  square  inch, 
which  a  thick,  hollow  cylinder  will  withstand,  the  inter- 
nal and  external  radii,  and  the  tenacity  of  the  material 
of  the  cylinder  being  given. 

Rule, — Divide  the  difference  of  the  squares  of  the 
radii,  and  multiply  the  quotient  by  the  tenacity  per 
square  inch  of  the  material  of  the  cylinder. 

Ex,  2. — The  internal  and  external  radii  of  a  thick, 
hollow  cylinder  being  respectively  nine  inches  and 
twenty-seven  inches,  and  the  tenacity  per  square  inch 
of  the  material  of  the  cylinder  ten  thousand  pounds, 


64  QUARTZ    OPERATOR'S 

what  fluid  pressure  per  square  inch  will  it  withstand  ? 
Gal.   Square  of  external  radius,  27X27=729 

Square  of  internal  radius,  9X9=81 

Difference  of  squares,  729 — 81=648 

Sum  of  squares,  729  +  81=810 

Then  10000X648-^810=8000  pounds.     Ans. 

SUSPENSION  RODS  OF  UNIFORM   STRENGTH. 

To  determine  the  transverse  section  at  any  point  of  a 
suspension  rod  of  uniform  strength  : 

Rule  1. — Divide  the  constant  weight  to  be  raised  by 
the  uniform  tension  per  square  inch,  due  the  tenacity  of 
the  material  in  the  rod,  and  multiply  the  quotient  by 
2,71828,  raised  to  a  power  equal  to  the  product  of  the 
length  of  the  rod  in  inches,  and  the  weight  of  one  cubic 
inch  of  the  rod,  divided  by  the  intensity  of  the  tension 
per  square  inch. 

Ex. — The  weight  to  be  raised  being  27000  pound?, 
the  intensity  per  square  inch  of  the  working  tension 
3,000,  the  weight  of  rod  per  cubic  inch  j\  of  a  pound, 
and  the  length  of  rod  600  feet.  Required  the  trans- 
verse section  at  the  upper  end  of  rod  ? 

GaL — Weight  divided  by  intensity  of  tension, 

27000^-3000=9 
Product   of  length  in   inches  and 

weight  of  cubic  inch, 7200X  A=2000 

This  product  divided  by  intensity 

of  tension, 2000—3000— =§ 


HAND    BOOK.  65 

Product  of  434295    and  last  quotient,  ,434295  X§= 

,289530. 

Number    corresponding   to   loga- 
rithm,  289530=1,94887 

And  1,94887X9=17,5983  inches.     Ans. 

TO  DETERMINE  THE  WEIGHT  OF  THE  ROD  THE  SAME 
DATA  BEING  GIVEN  AS  IN  EXAMPLE  UNDER  RULE 
ONE. 

Rule  2. — Multiply  the  transverse  section  by  the  in- 
tensity of  the  tension,  and  subtract  from  the  product  the 
constant  weight  to  be  raised. 

Ex. — The  transverse  section  being  17,5983  square 
inches,  as  determined  by  solution  of  example  one,  the 
intensity  of  tension  being  3,000  pounds  per  square  inch, 
and  the  constant  weight  to  be  raised  27,000  pounds, 
what  is  the  weight  of  the  rod  ? 

Cal  17,5983X3000=52794.9 

52794.9—27000.0=25794.9  pounds.     Ans. 

WATER   PIPES. 
To  determine  the   velocity  of  water  per  second,  flow- 
ing through  long  pipes,  the  head  or  hight  of  reservoir 
above  the  point  of  delivery,  the  length  and  diameter  of 
the  pipe  being  given. 

Rule. — Multiply  the  product  of  the  head  and  diame- 
ter of  the  pipe  in  feet  by  twenty-three  hundred.  Divide 
this  product  by  the  sum  of  once  the  length  and  fifty-two 


66  QUARTZ    OPERATOR'S 

times  the  diameter  of  the  pipe,  and  extract  the  square 
root  of  the  quotient. 

Ex. — The  head  is  six  hundred  feet ;  the  diameter  of 
pipe  nine  inches ;  the  length  of  pipe  six  thousand  feet ; 
what  is  the  velocity  of  the  water  per  minute  ? 

Cal. — Diameter  of  pipe  =9  inches=,75  feet. 

Product  of  head,  diameter,  etc.,  600X2300X>75= 
1035000,00. 

Sum  of  length  and  product,  6000+52X,75==6039 

Quotient,  1035000-^6039=171,386. 

Square  root  ^/i7i,386=13,09  feet,  velocity  per  sec. 

Per  minute,  13,09  X  60=785,4  feet.     Ans. 

Plane  Circular  Plates. — To  determine  the  grinding 
effects  by  one  revolution  of  a  plane  circular  plate  of  the 
usual  ring  form,  of  uniform  hardness,  about  its  axis  per- 
pendicular to  the  grinding  plane — the  greater  and  less 
diameters  and  pressure  per  square  inch  being  given. 

Rule. — Multiply  the  difference  of  the  fourth  powers 
of  the  radii  by  the  product  of  the  pressure  per  square 
inch,  and  the  square  of  the  ratio  between  the  radius 
and  circumference  of  a  circle,  and  divide  the  product  by 
the  greater  radius.  Deduced  from  formulas  4  and  5 
Discussion  of  Tractory,  etc.  6 

Ex. — The  greater  diameter  of  a  plane  circular  plate 
(muller)  of  the  usual  ring  form,  and  of  uniform  hard- 
ness, being  forty  inches;  the  less  diameter  sixteen  inches, 
and  the  pressure  per  square  inch  five  pounds,  what  is 
the  grinding  effect  by  one  revolution  ? 


HAND   BOOK.  67 

Cal.     48-v-2=24  greater  radius. 

16-=-2=8  less  radius. 
24X24X24X24X=331776  fourth  power  of  greater 
radius. 

8X8X8X8^=4096  fourth  power  of  less  radius. 
331776—4096=327680  difference  of  fourth  powers. 

22       22 

327680XyXyX5--24=674307.47.*    Ans. 

Conical  Plates. — To  determine  the  grinding  effect  by 
one  revolution  of  a  conical  plate  (muller)  of  the  usual 
ring  form,  of  uniform  hardness,  about  its  axis  perpen- 
dicular to  the  plane  of  the  base,  the  greater  and  less 
diameters  of  the  frustum,  the  height  of  the  cone  and  the 
pressure  per  square  inch,  parallel  with  the  axis  of  revo- 
lution being  given. 

Ride. — Multiply  the  square  root  of  the  sum  of  the 
squares  of  the  greater  radius,  and  height  of  the  cone  by 
the  difference  of  the  fourth  powers  of  the  radii,  and  this 
product  by  the  product  of  the  pressure  per  square  inch, 
and  the  square  of  the  ratio  between  the  diameter  and 
circumference  of  a  circle,  divided  by  the  square  of  the 
greater  radius.     Deduced  from  formulas  9  and  10. 

7  7 

Ex. — The  greater  diameter  of  a  conical  plate  (muller) 
of  the  usual  ring  or  frustum   form   being  forty-eight 

Remark. — The  unit  of  grinding  effect  here  taken  is  the  result 
of  a  body  impressing  one  square  inch  of  another  body,  with  on 
pound   pressure,   and  moving,   under  these    circumstances,  on 
inch.     See  Laws  of  Grinding,  Discussion  of  Tractory,  etc. 


68  QUARTZ    OPERATOR'S 

inches,  the  less  diameter  sixteen  inches,  the  height  of  the 
cone  twelve  inches,  the  pressure  per  square  inch,  parallel 
with  the  axis  of  revolution,  five  pounds,  what  is  the 
grinding  effect  by  one  revolution  ? 

Cat     48-f-2=24  greater  radius. 

16-^2=8  less  radius. 

24X24=576  square  of  greater  radius. 

12X12=144  square  of  hight  of  cone. 

j/ 576  + 144=26.8328  square  root  of  sum.* 

24X24X24X24=331776  fourth  power  of  greater  ra- 
dius. 

8X8X8X8=4096  fourth  power  of  less  radius. 

331776—4096=327680  difference  of  fourth  powers. 

327680X26.8328X2y2X2y2X5--576=753875.77. 

Ans. 

Tractory  Conoidal  Plates. — To  determine  the  grind- 
ing effect  by  one  revolution  of  a  tractory  conoidal  plate 
(muller)  of  frustum  form,  of  uniform  hardness,  about  its 
axis  perpendicular  to  the  plane  of  its  base,  the  greater 
and  less  diameters  of  the  frustum,  and  the  pressure 
per  square  inch  parallel  with  the  axis  of  revolution  be- 
ing given. 

Rule. — Multiply  the  difference  of  the  squares  of  the 
radii  of  the  frustum  by  twice  the  product  of  the  greater 
radius,  pressure  per  square  inch,  and  the  square  of  the 
ratio  between  the  diameter  and  circumference  of  a 
circle.     Deduced  from  formula  5. 

4 

Ex. — The  greater  diameter  of  a   tractory    conoidal 


HAND    BOOK.  69 

plate  (mullerj  being  forty-eight  inches,  the  less  diame- 
ters sixteen  inches,  and  the  pressure,  per  square  inch? 
five  pounds ;  what  is  the  grinding  effect  by  one  revo- 
lution. 

Cat.     48-4-2=24  greater  radius. 

16-^-2=8  less  radius. 

24X24=576  square  of  greater  radius. 

8X8=64  square  of  less  radius. 

576 — 64=512  difference  of  squares. 

5l2X24X5X272X2T2X2=1213753.47.    Ans. 

Remark. — Since,  in  this  style  of  plate,  the  wear  is 
perfectly  uniform,  the  grinding  effect  will  be  the  same, 
whether  the  central  opening  be  large  or  small,  providing 
the  weight  of  the  muller  be  the  same  in  each  case. 


MENS  UEATION. 

Prop.  1. — The  square  root  of  the  sum  of  the  squares 
of  the  base,  and  perpendicular  of  a  right-angled  triangle 
is  equal  to  the  hypothenuse. 

Ex. — The  base  of  a  right-angled  triangle  is  eight  feet, 
the  perpendicular  fifteen  feet,  what  is  the  hypothenuse  ? 

Gal.       8X8=64  15X15=225 

64+225=289  i/att±±l 7  feet.    Ans. 

Prop.  2. — The  square  root  of  the  difference  of  the 
squares  of  the  hypothenuse,  and  one  of  the  sides  of  a 
right  angled  triangle  is  equal  to  the  other  side. 


70  QUARTZ    OPERATOR'S 

Ex.  1. — The  hypothenuse  is  thirteen  feet,  the  perpen- 
dicular twelve  feet ;  what  is  the  base  ? 

Cal       13X13=169  12X12=144 

169—144=25  j/?7=5feet.     Ans. 

Ex.  2. — The  hypothenuse  is  thirty-seven  feet,  the 
base  twelve  feet ;  what  is  the  perpendicular  ? 

Cal.     37X37=1369  12X12=144 

1369—144=1225  1/ITiT=35  feet.  Ans. 

Prop.  3. — The  circumference  of  a  circle  is  equal  to 
twenty-two  times  the  diameter,  divided  by  seven? 
(nearly). 

Remark. — The  true  circumference  of  a  circle  lies 
between  3|J  and  3}f  times  the  diameter,  which  is 
nearly  3.1416.  This  ratio  is  usually  represented  in 
formulas  by  the  character  n. 

Ex. — The  diameter  of  a  circle  being  ten  feet,  what  is 
the  circumference  ? 

Cal     10X22--7=31.428,  or  10X3.1416=31.416. 

Ans. 

Prop.  4. — The  length  of  an  arc  of  a  circle  containing 
any  number  of  degrees  is  equal  to  the  product  of  the 
number  of  degrees  in  the  arc,  diameter  of  the  circle  and 
3.1416  divided  by  three  hundred  and  sixty. 

Ex. — What  is  the  length  of  an  arc  containing  seventy- 
five  degrees,  the  diameter  of  whose  circle  is  twenty-one. 

Gal.     75X21X3.1416--360=13.74feet.    Ans. 
•  Prop.  5 — The  length  of  an  arc  of  a  circle  is  equal  to 


HAND    BOOK.  71 

one-third  of  the  difference  between  eight  times  the  chord 
of  half  the  arc,  and  once  the  chord  of  the  arc. 

Ex. — Required  the  length  of  an  arc  whose  chord  is 
ten  feet,  and  the  chord  of  one-half  the  arc  is  5.177  feet  ? 

Cal.  5.177X8—10=31.416.  31.416-5-3=10.472 
feet.     Ans. 

Prop.  6 — The  diameter  of  a  circle  is  equal  to  the  sum 
of  the  hight  of  any  segment  of  the  circle,  and  one  third 
the  square  of  half  the  base  of  that  segment. 

Ex. — The  base  of  a  segment  of  a  wheel  is  fifty -four 
inches ;  the  hight  of  the  segment  three  inches  ;  what  is 
the  diameter  of  the  wheel. 

Cal.  54--2=27     27X27-5-3=243 
243  +  3=246  inches.     Ans. 

Prop.  7. — The  length  of  the  common  cycloid  is  equal 
to  four  times  the  diameter  of  the  generating  circle. 

Ex. — What  is  the  length  of  a  common  cycloid,  the 
length  of  whose  generating  circle  is  five  feet  ? 

Cal.     5X4=20  feet.     Ans. 

Prop.  8. — The  hight  of  a  common  parabola  is  equal  to 
the  square  of  half  the  base,  or  the  square  of  the  ordinate 
divided  by  twice  the  parameter. 

Ex. — The  base  of  a  common  parabola  is  eight  feet ; 
the  perameter  four  thirds  of  a  foot ;  wThat  is  its  hight  ? 

Cal  8-5-2=4     4X4=16 

4X2-^-3=8-r-3     16X3-5-8=6  feet.    Ans. 


72  QUARTZ    OPERATOR'S 

Prop.  9. — The  length  of  an  arc  of  the  common  para- 
bola, measured  from  its  vertex,  is  as  follows : 

Length  of  arc.       =y  |/p2  +  y2  +p_log  (y  +  i/p2+y2-) 
~2p  "2    ,    (  p 

Ex. — The  half  base  or  coordinate  (y)  being  twelve 
feet,  and  the  half  parameter  (p)  being  five  feet,  what  is 
the  length  of  the  arc  of  the  parabola,  measured  from  the 
vertex  ? 

Cat.  12X12=144     5X5=25 
144+25=169     j/I^IS 
13X12-5-10=15.6     13  +  12=25 
25-1-5=5     Naperian  log,  5-.1.61 
1,61X5-^-2=4.02    15.6  +  4.02= 
Prop.  10. — An   ordinate  of  an  ellipse  is  equal  to  the 
product  of  the  minor  axis,  and  the  square  root  of  the 
difference  of  the  squares  of  the  major  axis,  and  the  co- 
ordinate divided  by  the  major  axis. 

Ex. — The  axes  of  an  ellipse  are  seven  and  ten  feet 
An  ordinate  is  six  feet ;  what  is  the  coordinate.  ? 
Cal.     10X10=100      6X6=36 
100—36=64         !/64=8 
8X7-^-10=5.6  feet.     Ans. 
Prop.  11. — The    circumference   of  an    ellipse  is    as 
follows : 

2  4  6 

Circumference  =2  11  A  (1 — f — }f~ jftfgSr—  etc)- 

Remark. — In  the  above  formula,  A  denotes  the  semi- 
major   axis ;  E  the  eccentricity ;  that  is,  the  distance 


HAND   BOOK.  73 

between  the  centre  and  one  of  the  foci  of  the  ellipse, 

divided  by  the  semi-major  axis. 

2  4 

Ex.     E-h4=,01.        EX3-^64=,00G075. 

EX45-t-2304=,000001. 

.01  +000075  +  ,000001=  010076 
1_.010076=,989924 

.989924X2X20—2X3.1416=62.1989  feet.     Ans. 

Prop.  12. — An  ordinate  of  an  hyperbola  is  equal  to 
the  product  of  the  conjugate  axis,  and  the  square  root 
of  the  difference  of  the  squares  of  the  co-ordinate  and 
transverse  axis,  divided  by  the  transverse  axis. 

Ex. — The  transverse  axis  of  an  hyperbola  is  four 
feet ;  the  conjugate  axis  three  feet,  and  an  ordinate  on 
the  transverse  axis  and  hight  of  the  hyperbola  ten 
feet ;  what  is  the  co-ordinate  ? 

Cat.     10X10=100     4X4=16     100—16=84 

y'(84)=9.165     9.165X3^-4=6.874  feet.     Ans. 

Prop  13. — The  length  of  an  hyperbola  is  as  follows, 
to  wit : 

=iiA[l-i(2-E2)-A(2-EV-rffe(2-E2  )*  ] 
Remark. — In  the  above  formula,  A  represents  the 

semi-transverse   axis  ;  E   the  eccentricity ;  that  is,  the 

distance  of  the  center  from  one  of  the  foci  divided  by 

the  semi-transverse  axis. 

Ex. — The  difference  of  the  distances  of  a  point  in  the 

curve,  from  the  foci,  being  twenty  feet,  and  the  distance 

D 


74  QUARTZ    OPERATOR'S 

from  the  center  from  one  of  the  foci,  fifteen  feet,  what  is 
the  length  of  the  hyperbola  ? 

Col.  20-r2=10.     15-^10=E.     Eccentricity. 
— (2— E  )-Ht  =  +  ,1875  ;  3(2-E2)  2--64=-,0264 

2    3 

—45  (2-E  )  -^2304=  +  .0082  1.+.1875+.0082 
—,0264=1.1693 

1.1693X10X3.1416=36.7347  feet.     Ans. 

Prop.  14. — The  length  of  the  spiral  of  Archimedes  is 
as  follows : 

Length.^  <J  t  V  (1+t  )+log[i/(l+/)+<]  )■ 

JRemarh. — In  the  above  formula,  (t)  represents  the 
measuring  arc,  and  (A)  the  relation  between  the  radius 
vector  and  measuring  arc. 

Ex. — The  measuring  arc  being  the  entire  circle,  and 
the  radius  vector  unity,  what  is  the  length  of  the  spiral 
or  spire  ? 

Cal.     15  =  112=6,2832.     a  =  -^1-l  =  ^^ 
£l/l+4X(3,1416)2==3,1811 

,  log  [i/l+4X  {3.1416)2  +  2X3.1416]~2019 


4X3,1416 

3.181 1  -+-,2019=3.383.     Ans. 

Ex.  2. — The  measuring  arc  being  twice  the  circumfer- 
ence of  a  circle  whose  radius  is  unity,  what  is  the  length 
of  the  spiral,  and  what  is  the  length  of  the  second  spire  ? 


HAND    BOOK.  75 

Cal.     t  =4n ;         flt=r=jjj  a  constant  quantity. 

V/l  +  l6X(3.l4i6)2^-12.6060 
4X§^4i6log  Cv/i  +  i6X(3.i4i6)2  +  4X3.1416]=?2567 

12,6060+,  2567=12,8627  length  of  spiral.        Ans. 

The  first  spire,  as  found,  for  example  one,  is  3.383. 

Hence,  12.8627—3.383=9,4797  length  of  second 
spire.     Ans. 

Prop.  15. — The  area  of  a  square,  a  rectangle,  or  a 
parallelogram,  is  equal  to  the  product  of  its  base  and 
altitude. 

Ex. — What  is  the  area  of  a  fljor  forty-five  feet  by 
one  hundred  and  twenty-five  feet  ? 

Cal.     125X45=5625  square  feet.     Ans. 

Prop.  16. — The  area  of  a  triangle  is  equal  to  half 
the  product  of  the  base  and  perpendicular. 

i&r.— What  is  the  area  of  a  triangle  whose  base  is 
twelve  feet,  and  altitude  eighteen  feet  ? 

Cal.     12X18-^2=108  square  feet.     Ans. 

Prop.  17. — The  area  of  a  trapezoid  is  equal  to  half 
the  product  of  the  sum  of  the  two  parallel  sides  and  the 
altitude. 

Ex. — The  parallel  sides  being  thirteen  feet  and  sev- 
enteen feet,  and  their  distance  apart  seven  feet,  what  is 
the  area  of  the  trapezoid  ? 

Cal.     134-17=30.     30X7^-2=105  square  feet. 

Ans. 

Prop.  18. — The  area  of  an  irregular  polygon  is  equal 

d2 


76 


QUARTZ    OPERATOR'S 


to  the  sum  of  the  areas  of  the  separate  triangles  com- 
posing it. 

TABLE. 


Triangle, 3 ,43301 27 

Square 4 1,0000000 

Pentagon, 5 1 ,7204774 

Hexagon, 6 2,5980762 

Heptagon,  . .  .7 3,6339124 


NAMES.       SIDES. 


AREAS. 


Octagon 8 4,8284271 

Nonagon 9 6,1818242 

Decagon,..    10 7,6942088 

Undecagon  .11 9,3656399 

Dodecagon..  12 11,1961524 


Prop.  19. — The  area  of  a  regular  polygon  is  equal  to 
the  square  of  one  of  its  sides  multiplied  by  the  area  of  a 
polygon  of  the  same  number  of  sides,  and  whose  side 
are  unity. 

Ex. — What  is  the  area  of  a  nonagon  whose  side  is 
ten  feet  ? 

pal     10X10=100.     Tabular  area  =6,1818242 

6,1818242X100=618,18242  square  feet.     Ans. 

Prop.  20. — The  area  of  a  circle  is  equal  to  one  fourth 
the  product  of  the  diameter  and  circumference ;  also 
equal  to  the  product  of  the  square  of  the  diameter  and 
,7854 ;  and  also  equal  to  the  square  of  the  diameter  and 
eleven  divided  by  fourteen. 

Ex. — What  is  the  area  of  a  circle  whose  diameter  is 
forty  feet  ? 

Gal.     40X40X11-5-14=1257,14  square  feet.     Ans. 

Prop.  21. — The  area  of  a  sector  of  a  circle  is  equal 
to  half  the  arc  of  the  sector  multiplied  by  half  the  di- 
ameter of  the  circle. 


HAND    BOOK.  77 

Ex, — What  is  the  area  of  a  sector  whose  arc  is  forty- 
degrees,  and  the  diameter  of  the  circle  thirty  feet. 

Cal.     3.1416X40--360X30=10.472 

10.472-=-2X  15=78.54  square  feet.     Ans. 

Prop,  22. — The  area  of  a  circuWring  is  equal  to  the 
difference  of  the  squares  of  the  diameters  multiplied  by 
,7854. 

Ex. — What  is  the  area  of  a  circular  ring  whose  great- 
er diameter  is  forty-two  feet,  and  less  diameter  seven 
feet? 

Cal     42X42=1764.         7X7=49. 

1764—49=1715.  171oX,7854=1346,96  square 
feet.     Ans. 

Prop.  23. — The  area  of  the  common  cycloid  is  equal 
to  three  times  the  area  of  the  generating  circle. 

Ex. — What  is  the  area  of  a  common  cycloid,  the  di- 
ameter of  whose  generating  circle  is  seven  feet  ? 

Cal.     7X7X11-M  4X3=115.5  square  feet.     Ans. 

Prop.  24. — The  area  of  the  common  parabola  is  equal 
to  two-thirds  the  product  of  the  base  and  altitude. 

Ex. — The  base  of  a  common  parabola  is  twelve  feet, 
and  the  hight  fifteen  feet,  what  is  the  area  ? 

Cal.     12X15X2^-3=  120  square  feet.     Ans. 

Prop.  25. — The  area  of  an  ellipse  is  equal  to  the  pro- 
duct of  the  semi-diameters  multiplied  by  3.1416. 

Ex. — What  is  the  area  of  an  ellipse,  the  semi-diame- 
ters being  ten  feet  and  eight  feet  ? 

Cal.     10X8X3.1416=251.328  square  {eet.     Ans. 

b3 


78  QUARTZ    OPERATOR'S 

Prop,  26. — The  area  of  an  hyperbola  is  as  follows  : 

Area  =ay—AXB  log  (^•+-g) 

Remark. — In  this  formula,  A  represents  the  semi- 
transverse  axis,  B  the  conjugate  axis,  x  and  y  the  gen- 
eral co-ordinates. 

Ex. — Given  the  base,  13,748  feet,  the  hight  six  feet, 
transverse  axis   eight  feet,  and  the  conjugate  axis  six 
feet,  what  is  the  area  of  the  hyperbola  ? 
Cal.     A=8-i-2=4  semi-transverse  axis. 
B=6-i-2=3  semi-conjugate  axis. 
#=6  +  4—10  co-ordinate. 
#=13.748-^-2=6.874  co-ordinate. 
Then  area=68.74— 12  log  4.791=49.88  square  feet. 

Ans. 
Prop.  27. — The  area  of  the  equable  spiral  or  spiral 
of  Archimedes,  is  equal  to  one-third  the  difference  be- 
tween the  cube  of  the  number  of  revolutions  and  the 
cube  of  a  number  one  less  than  that  of  the  revolutions, 
multiplied  by  3.1416. 

Ex. — What  is  the  area  of  an  equable  spiral,  whose 
radius  vector  is  seven  feet,  described  by  seven  revolu- 
tions ? 

Cal.     7X7X7=343  cube  of  revolutions  =n3 

6X6X6=216  cube  of  number  one  less=(w-l)3 
Then  343=216=127  difference  =n3— (n-1)3 

127X3,14.16-^-3=132.99  square  feet.     Ans. 
Prop.  28. — The  area  of  an  irregular  plane  surface  is 
equal  to  one- third  the  distance  between   any  two  con- 


HAND    BOOK.  79 

secutive  ordinates  multiplied  by  the  sum  of  the  extreme 
ordinates,  increased  by  four  times  that  of  the  even  or- 
dinates, and  twice  that  of  the  uneven  ordinates. 

Remark. — The  entire  number  of  ordinates  or  perpen- 
diculars is  to  be  uneven,  and  at  equal  distances  apart. 
Fig.!.  Ex.     Having  given 

-    i  as  in  figure  1,  the  base 

PAB,  equal  to  o40  feet> 
and  having  found  the 
perpendiculars  AD  = 
50,  a2  e3  =  55,  as  e3  =  80,  a4  e4  =  100,  a5  e5  =  120, 
aGeG  =  110,  a7  e7  =  115,  a8e8  =  130,  a9  e9  =  128, 
«io*io  =  90>  011*11=  HO,  aueu  =  108,  aiz  eu  =  75 
feet,  what  is  the  area  of  ABCD  ? 

Cal.    540-^-12=45  distance  apart  of  perpendiculars. 

45-^3=15  one-third  distance  between  any  two  per- 
pendiculars. 

50+75=125  sum  of  extremes. 

55+100+110+130+90+108=593  sum  of  even 
ordinates  or  perpendiculars. 

80+120+115+128+110=553  sum  of  uneven  or- 
dinates or  perpendiculars. 

593X4=2372;  553X2=1106. 

125+2372+1106=3603. 

3603xi5=Area  of  ABCD,=54045  square  feet. 
Ans. 

Prop.  29. — The  area  or  convex  surface   of  a  right 

d4 


80  QUARTZ    OPERATOR'S 

prism,  or  of  a  cylinder,  is  equal  to  the  primeter  of  the 
base  multiplied  by  the  altitude. 

Ex. — What  is  the  convex  surface  of  a  cylinder  whose 
diameter  is  seven  feet  and  length  ten  feet  ? 

Col.  7X22-^7=22;  22X10=220  square  feet. 
Ans. 

Prop.  30. — The  area  or  convex  surface  of  a  right 
pyramid  or  cone  is  equal  to  the  perimeter  of  the  base 
multiplied  by  one  half  of  the  slant  height. 

Ex. — What  is  the  area  or  convex  surface  of  a  cone 
whose  slant  height  is  twenty  feet,  and  the  diameter  of 
whose  base  is  seven  feet  ? 

Gal.  7  X  22—7=22  ;  22  X  20-r-2=220  square  feet. 
Ans. 

Prop.  31. — The  area  or  convex  surface  of  a  spheri- 
cal zone  is  equal  to  the  altitude  of  the  zone  multiplied 
by  the  circumference  of  a  great  circle  of  the  sphere. 

Ex. — The  height  of  a  zone  is  eight  feet,  the  diameter 
of  the  sphere  twenty-five  feet.  What  is  the  area  of  the 
zone  ? 

Cat.     8X25X3.1416=628,32  square  feet.     Ans. 

Prop.  32. — The  area  of  a  sphere  is  equal  to  the  pro- 
duct of  the  diameter  and  circumference. 

Ex. — What  is  the  area  of  a  ball  ten  inches  in  diam- 
eter ? 

Cat.  10X3.1416=31.416;  31.416X10=314.16 
square  feet.     Ans. 


HAND    BOOK.  81 

Prop.  33. — The  area  or  surface  described  by  revolv- 
ing a  cycloid  about  its  base  is  sixty-four  thirds  of  the 
generating  circle. 

Ex. — What  is  the  area  or  surface  described  by  the 
revolution  of  a  cycloid  about  its  base,  the  diameter  of 
the  generating  circle  being  seven  feet  ? 

Cat.  7X22-^4=38.5;  38.5x64-^3=821.33  square 
feet.     Ans. 

Prop.  34. — The  area  or  convex  surface  of  a  parabo- 
loid is  as  follows : 


Area=i^jA+^Y--il} 
3      IV       4A2y         8A2) 


Remark. — In  this  formula  b  represents  one-half  the 
diameter  of  the  base,  h  the  height  of  the  paraboloid, 
and  ii=3.1416. 

Ex. — The  diameter  of  the  base  of  a  paraboloid  being 
six  feet,  and  the  height  two  feet,  what  is  the  surface  of 
revolution  ? 

Cat.     4X6-f-2x2X3.1416-f-3=25.1328. 

I         v   3. 


(-4) 


125  27       27       125     27     98 


64        8X8     64        64      64     64 
25.1328  X98-v-64=38.48  square  feet.     Ans. 
Prop.  35. — The  area  of  an  ellipsoid  described  by  re- 
volving an  ellipse  about  its  major  axis,  is  as  follows : 

2  4  6 

Arearz4nAB  (  1  -±-±—±—  &C.) 

\  6  40         113  / 

»5 


82  QUARTZ    OPERATOR'S 

Ex. — The  major  axis  being  twenty  feet,  and  the 
eccentricity  four-tenths  of  a  foot,  what  is  the  area  of 
the  ellipsoid? 

Gal.     B^zj/(100 — lG)n9.1G5  semi-conjugate  axis, 
4X3.1416X10X9.16SX(1— .0167— .0064— &c.)= 
1113.59  square  feet.     Ans. 

Prop.  36. — The  convex  surface  of  a  hyperboloid  is 
as  follows : 

Ayw=—  J  x  j/(  x*  —  a2)  —  A !/(  A2— a2  ) 
+aHog  [A+1/(A2-a_2)    | 

Remark. — In  the  above  formula,  (A)  represents  the 
transverse  axis}  (B)  the  conjugate  axis;  (x)  an  ordi- 
nate on  the  axis  of  revolution;  and,  (a)  equal  to  the 
square  root  of  A4 

A9+Ba" 

Ex. — The  transverse  axis  (A)  is  four  feet,  the  conju- 
gate axis  (B)  three  feet,  and  the  hight  six  feet ;  what  is 
the  area  of  the  hyperboloid  ? 

Gal.     0=4+6=10.         a=J£.         a2=W. 
15X3.1416  (94.742.-9.6— 11.397)=217.31  square 

feet.    Ans. 

Prop.  37. — The  solid  contents  of  a  prism,  or  of  a 


HAND    BOOK.  83 

cylinder,  are  equal  to  the  area  of  the  base  multiplied  by 
the  altitude. 

Ex. — The  diameter  of  a  cylinder  is  twenty-one  inches 
and  its  length  forty  inches  ;  what  are  the  solid  contents  ? 

Gal.     21--7X22=66;         6  6X21 --4:=  346.5 
346.5X40.-^13860  solid  inches.     Ans. 

Prop.  38. — The  solid  contents  of  a  pyramid,  or  of  a 
cone,  are  equal  to  the  base  multiplied  by  one-third  of 
the  altitude. 

]$x. — The  square  inches  in  the  base  of  a  cone  are 
346.5,  and  the  hight  forty  inches;  what  are  the  solid 
contents  ? 

Gal     346.5X40-^-3=^4620  solid  inches.     Ans. 

Prop.  39. — The  solid  contents  of  a  frustum  of  a  pyra- 
mid, or  a  cone,  are  equal  to  one-third  of  the  altitude  of 
the  frustum,  multiplied  by  the  sum  of  the  two  bases,  in- 
creased by  a  mean  proportional  between  them. 

J£x. — What  is  the  solidity  of  the  frustum  of  a  cone 
whose  lower  diameter  is  ten  inches,  upper  diameter 
eight  inches,  and  hight  twenty-four  inches  ? 

Gal.     10X10=100         8X8=64         10X8=80 
100  +  64+80=244;    244X,?584X24--3=1 533.10  solid 
inches.     Ans. 

Prop.  40. — The  solidity  of  a  sphere  is  equal  to  one- 
third  of  the  area  of  a  great  circle,  multiplied  by  the 
radius  ;  or,  it  is  equal  to  the  cube  of  the  diameter,  mul- 
tiplied by  ,5236. 

d6 


84  QUARTZ    OPERATOR'S 

Ex. — What  is  the  solidity  of  a  ball  fourteen  inches 
in  diameter? 

Gal.  14x22-^-7=44;  14X44X14-^-6=1437.33 
cubic  inches.     Ans. 

Prop.  41. — The  solidity  of  a  spherical  segment  is 
equal  to  one-half  the  hight  of  the  segment  multiplied 
by  the  sum  of  the  areas  of  the  two  basis ;  and  this  pro- 
duct increased  by  the  solid  contents  of  a  sphere  whose 
diameter  is  equal  to  the  hight  of  the  segment. 

Remark. — If  the  segment  has  but  one  base,  the  other 
is  to  be  regarded  equal  to  0  (zero). 

Ex. — What  is  the  solidity  of  a  spherical  segment,  the 
diameter  of  the  sphere  being  forty  inches,  and  the  dis- 
tances from  the  center  to  the  bases  sixteen  inches,  and 
ten  inches  ? 

Cal.  20X20=400;  16X16=256;  10X10=100; 
400—256=144;  400—100=300;  144+300=444; 
444X4=1776;  1776X,7854=1394.8704;  1394,8704 
X3=4184.6112 ;  6X6X6X,5236=113.0976 ;  4184 
,6112+113.0976=4297.7088  solid  inches.     Ans, 

Prop.  42. — The  solidity  of  a  regular  polyedron  is 
equal  to  the  cube  of  one  of  its  edges  multiplied  by  the 
solidity  of  a  similar  polyedron  whose  edge  is  one. 


HAND    BOOK.  85 

Table  of  Regular  Polyedrons  "whose  edges  are  one. 


Names. 

No.  of 
Faces. 

Surface. 

Solidity. 

Tetraedron.  .  . 
Hexaedron.  .  . 
Octaedron.  .    . 
Dodecaedron . . 
Icosaedron. . . . 

4 

6 

8 

12 

20 

1.7320508 
6.0000000 
3.4641016 
20.6457288 
8.6602540 

0.1178513 
1.0000000 
0.4714045 
7.6631189 
2.1816950 

Ex. — What  is  the  solidity  of  an  icosaedron  whose 
edge  is  twenty  inches  ? 

Cal.  20X20X20X2.1816950=17453.56  solid  inches. 

Ans. 

Prop.  43. — The  solidity  of  a  solid,  generated  by  the 
revolution  of  the  cycloid  about  its  base,  is  equal  to  five- 
eighths  of  a  cylinder  whose  length  is  equal  to  the  base 
of  the  cycloid,  and  whose  diameter  is  twice  that  of  the 
generating  circle. 

Ex. — What  is  the  solidity  of  a  solid,  generated  by  the 
revolution  of  a  cycloid  about  its  base,  the  diameter  of 
whose  generating  circle  is  seven  feet  ? 

Cal  7X22-^7=22  length  of  solid,  7X2=14  diameter, 
7X22=154;  154X22X5--8=2117.5  solid  feet.    Ans. 

Prop.  44. — The  solidity  of  a  paraboloid  is  equal  to 
one-half  of  the  solid  contents  of  a  cylinder  of  the  same 
hight,  and  same  base  as  the  paraboloid. 


86  QUARTZ    OPERATOR'S 

Ex. — What  are  the  solid  contents  of  a  paraboloid,  the 
diameter  of  whose  base  is  twenty-eight  inches,  and 
height  forty  inches  ? 

Gal.     28X22^-7=88;         88X28--4=616; 
616x40-^-2=12320  solid  inches.     Ans. 

Prop.  45. — The  solidity  of  a  spheroid  is  equal  to 
two-thirds  the  solidity  of  a  circumscribing  cylinder. 

Ex.  1. — What  is  the  solidity  of  an  oblate  spheroid 
whose  major  diameter  is  twenty-eight  inches,  and 
minor  diameter  twenty-one  inches  ? 

Gal     (28X88--4)X(21X2--3)=8624  solid  inches. 

Ans. 

Ex.  2. — What  is  the  solidity  of  a  prolate  spheroid, 
the  diameters  being  as  in  example  1. 

Gal.     (2lX66-=-4)X(28X2--3)=6468  solid  inches. 

Ans. 

Prop.  46. — The  solidity  of  an  hyperboloid  is  as 
follows : 


Solidity.^  (—^-A2a0 


Remark. — In  this  formula  the  transverse  and  conju- 
gate axes  are  respectively  represented  by  (A)  and  (B), 
and  the  ordinate  on  the  axis  of  revolution  by  (#). 

Ex. — What  is  the  solidity  of  an  hyperboloid  whose 
transverse  axis  is  four  feet,  conjugate  axis  three  feet, 
and  hight  six  feet  ? 


HAND    BOOK.  87 

Cat.  6  +  4=10;  3.1416X94-16=1.76715;  1000 
+  128=1128  ;  1128--3=376  ;  376—160=216  ; 
1.76715X216=381.7  solid  feet     Ans. 

Remark. — The  relations  of  the  co-ordinates  to  each 
other  in  the  tractory  curve,  the  length  of  the  curve,  the 
quadrature  of  the  meridian  plane  coinciding  with  the 
axis,  the  surface  of  revolution  of  the  tractory  conoid ; 
and  the  solid  contents  of  that  solid  will  be  found  under 
the  heading  "  Discussion  of  the  Tractory  and  differently 
formed  Grinding  Plates." 

INVOLUTION. 

Involution  is  the  raising  of  quantities  to  any  proposed 
power. 

The  power  of  any  quantity  is  that  quantity  multi- 
plied any  number  of  times  by  itself. 

Thus,         3X3=9  is  the  second  power  of  3  ; 

5X5X5=125  is  the  third  power  of  5. 

The  power  is  sometimes  expressed  by  writing  the 
quantity  with  the  number  of  the  power  a  little  above  it, 
and  at  the  right  hand. 

Thus,  to  express  the  power,  write 
32=3X3=9  square  of  3. 
53=5X5X5=125  cube  of  5. 
27=2X2X2X2X2X2X2=128  seventh  power  of  2. 

The  number  of  the  power,  as  2,  3,  7  above,  is  termed 
the  exponent  or  index. 

EVOLUTION. 
Evolution  is  the  extracting  of  roots. 


88  QUARTZ    OPERATOR^ 

The  root  of  any  quantity  is  a  quantity  which,  if  mul- 
tiplied by  itself  a  certain  number  of  times,  produces  the 
original  quantity;  and  is  called  the  second  or  square 
root,  the  third  or  cube  root,  etc.,  according  to  the  num- 
ber of  multiplications. 

Thus  the  second  or  square  root  of  9  is  a  quantity 
whose  square  or  second  power  produces  9 — that  is 
3.  And  the  seventh  root  of  1 28  is  a  quantity  whose 
seventh  power  produces  128 — that  is  2. 

Roots  are  sometimes  represented  by  the  symbol  j/, 
with  the  number  of  the  root  written  within  the  angle  of 
the  symbol,  and  sometimes  by  exponents  or  indices. 

Thus  the  square  root  is  represented 

2     —  1 

|/9— 9^=3         and  is  read  square  root  or  half  power 

of 

i 

j!K9i 25=1 25^=5  and  is  read   cube  root   or  one-third 

power  of  125. 

7  1 

-j/ 128=1 28  =2  and  is  read  seventh  root  or  one- 
seventh  power  of  128. 

The  number  2  within  the  angle  of  the  symbol  in  ex- 
pressing the  square  root,  is  usually  omitted. 

Both  involution  and  evolution  are  sometimes  expressed 
by  fractional  exponents  or  indices. 

3 

Thus  32^  The  numerator  shows  that  the  quantity 
is  to  be  raised  to  the  third  power,  32X32X32=32768, 
and  the  denominator  shows  that  the  fifth  root  of  that 

5   1 

power  is  to  be  extracted — ^32768=32768  =8. 


HAND    BOOK.  «y 

Or  the  denominator  shows  that  the  fifth  root  of  the 

quantity  is  to  be  extracted  j/32=32F=2. 

And  the  numerator  shows  that  the  root  thus  obtained 
is  to  be  cubed  or  raised  to  the  third  power,  2  X  2  X  2=8. 
TO  EXTRACT  ANY  ROOT   OF  A  POWER  OR  QUALITY. 

Rule. — 1st.  Point  off  the  given  power  or  quantity 
into  periods,  containing  each,  except  the  left-hand  period, 
as  many  figures  as  the  required  root  indicates,  beginning 
at  the  units  place  and  pointing  to  the  left  in  integers  and 
to  the  right  in  decimals. 

2d.  Find  by  trial  the  first  figure  of  the  root  and  set  it 
to  the  right  of  the  quantity  or  power  in  the  quotient's  or 
root's  place.  Also  place  its  first  power  at  the  head  of 
a  column  on  the  extreme  left,  and  its  successive  higher 
powers  (regularly  increasing  the  exponents  by  onej  at 
the  heads  of  columns  following  in  order  toward  the  right ; 
thus  forming  as  many  columns  as  there  are  units  in  the 
exponent  of  the  power  whose  root  is  sought.  The 
highest  power  of  the  first  root  figure  falls  under  the  left- 
hand  period  of  the  quantity,  and  is  to  be  subtracted 
therefrom,  and  with  the  remainder  the  next  period  is  to 
be  brought  down. 

3d.  Add  the  root  figure  to  the  first  column,  and  mul- 
tiply this  sum  by  the  root  figure,  placing  the  product  in 
the  next  right  hand  column  and  adding  it  thereto.  Mul- 
tiply this  sum  by  the  root  figure,  placing  the  product  in 
the  next  right  hand  column,  which  add  thereto,  and  thus 
proceed   adding  and  multiplying  until  the   number  of 


90  QUARTZ    OPERATOR'S 

additions  shall  be  one  less  than  the  exponent  of  the 
number  whose  root  is  sought.  The  number  thus  found  is 
termed  the  trial  divisor.  The  root  figure  is  to  be  added 
to  the  first  column  (the  successive  multiplications  and 
additions  following  as  above,  except  that  one  multiplica- 
tion less  is  made  each  time)  as  many  times  as  there  are 
units  in  the  exponent  of  the  number  whose  root  is 
sought. 

4th.  Find  how  many  times  the  trial  divisor  is  con- 
tained in  the  remainder,  with  the  first  left  hand  figure  of 
the  next  period  brought  down,  and  place  the  quotient  as 
a  second  root  figure.  Also  add  this  root  figure,  removed 
one  place  to  the  right,  to  the  first  column.  Multiply 
the  sum  thus  obtained  by  this  root  figure,  adding  the 
product,  removed  two  places  to  the  right,  to  the  second 
column.  Thus  continue  to  multiply  and  add  to  the  suc- 
cessive columns,  removing  the  product  at  each  addition 
one  figure  further  to  the  right,  until  the  product,  falling 
under  the  quantity  whose  root  is  sought,  is  to  be  sub- 
tracted therefrom,  and  the  remainder  with  the  next 
period  brought  down  as  before. 

5th.  In  a  similar  manner  the  successive  figures  of  the 
root  are  determined. 


HAND    BOOK.  91 

Example  1st  Required  the  side  of  a  square  inclosure 
containing  55225  square  rods.     Ans.  235  rods. 


Cal. 


/  /  / 

55225  [235 

2 

4 

2 

152 

43 

129 

3 



2325 

465 

2325 

Ex.  2d.  Required  the  side  of  a  cubical  reservoir  con- 
taining 9663597  solid  inches.     Ans.  213  inches. 


Cal. 

9663597  [213 

2 

4 

8 

2 

8 

- 

1663 

4 

1261 

1261 

2 

62 

402597 

61 

1323 

402597 

1 

1899 

62 

134199 

1 

633 


92  QUARTZ    OPERATOR'S 

Ex.  3d.  Required  the  fifth  root  of  6436343.  Ans.  23. 


Cal 

6436343  [23 

2 

4 

8 

16     32 

2 

8 

24 

64 

4 

12 

32 

80     3236343 

2 

12 

48 

278781  3236343 

6 

24 

80 

1078781 

2 

16 

12  927 

8 

40 

92927 

2 

309 

103 

4309 

DISCUSSION  OF  THE  TRACTORY  AND 
DIFFERENTLY  FORMED  GRINDING 
PLATES. 

The  discovery  of  the  Tractory  Curve  was  long  at- 
tributed to  Huygens,  an  eminent  mathematician  of  the 
seventeenth  century.  That  the  curve,  however,  was 
known  long  prior  to  the  discovery  of  Huygens,  is  proven 
by  recent  excavations  in  the  ruins  of  Pompeii,  where  has 
been  found  a  mill  whose  grinding  surfaces  are  of  trac- 
tory conoidal  form. 


HAND    BOOK.  93 

What  properties  of  the  curve  Huygens  may  have  in- 
vestigated does  not  appear.  D'Alembert  says  that  the 
e volute  of  the  curve  is  the  common  catenary.  Dr. 
Peacock  says  that  the  Tractory  is  an  inverted  semi- 
cycloid.  As  the  term  cycloid  here  used  is  not  qualified, 
it  must  be  inferred  that  the  common  is  meant.  Now, 
D'Alembert  and  Dr.  Peacock  cannot  both  be  right ;  for 
the  involute  of  the  common  cycloid  is  similar  and  equal 
to  the  evolute,  that  is,  the  cycloid  itself.  But  the  cycloid 
is  essentially  dissimilar  and  unequal  to  the  catenary. 
Therefore,  the  cycloid  and  the  involute  of  the  catenary 
cannot  both  coincide  with,  or  be  the  Tractory. 

Again,  as  the  equations  of  the  Tractory,  Catenary  and 
cycloid,  are  essentially  different,  it  is  evident  that  neither 
D'Alembert,  nor  Dr.  Peacock  has  correctly  demon- 
strated and  set  forth  the  properties  of  the  Ttractory. 

The  discrepancy  of  the  above  named  authors,  and  the 
unsatisfactory  and  unreliable  manner  of  laying  down 
the  curve  mechanically,  as  adopted  by  C.  Schiele,  of 
Oldham,  have  led  to  the  following  discussion,  the  cor- 
rectness of  the  result  of  which  is  not  only  certified  to  by 
several  distinguished  mathematicians,  but  is  farther  con- 
firmed by  numerous  and  carefully  made  experiments. 

A  tractory  is  defined  to  be  "  A  curve  whose  tangent 
is  always  equal  to  a  given  line." 

The  directrix  of  the  tractory  here  investigated  is 
parallel  with  one  of  the  axes,  and  the  point  of  origin  of 
the  curve  is  in  a  line  at  right  angles  to  the  directrix. 


94 


QUARTZ    OPERATOR'S 


2'iq.l. 


Let  A  Fig.  1  be  the  point 
of  origin. 

Lay  off  on  the  axis  AY 
the  constant  tangent  AF=a. 

Draw  the  directrix  FD; 
parallel  with  the  axis  AX. 

Draw  CD=a  tangent  to 
the  curve  ACC  at  the  point  C 

Produce  BC  in  a  right  line 
intersecting  FD  in  E. 

Let  x  and  y  be  co-ordinates 
of  the  curve  at  any  point  C, 
and  let  z  denote  the  length  of 
the  curve  AC. 


Then  CE=BE— BC=a— y,   and  EDS(cB— Cl)* 


: r a 

C'\ 


1.  By  similar  triangles 

2.  By  similar  triangles] 


=  {2ay-f) 

dX^Z^\ 


a—y 


dy 


dz=a^ 

a—y 

lv  Putting  u=(2ay- tffi 

22.  Squaring  Eq.  lx,  u2=     2ay — y2 

3r  Differentiating  Eq.  2lf  2udu=2ady — 2ydy 

udu 


4X.  Dividing  Eq.  82,  by  2  (a—y)  dy=- 


5V  Transposing  Eq.  2l?        y2 — 2ay~- 


a—y 


HAND    BOOK.  95 

6^  Completing  square  to  Eq.  51?  y1 — 2ay-\-a2=a2 — u2 
lv  Extracting  sq.  root  Eq.  619       y — a=±^/(a2 — u2) 
Sx.  Or,  a— y=±v/(a2— u2) 

3.  Transposing  Eq.  719  y=a  +  i/(a2 — u2) 
9j.  Substituting  value  of  (a — y)  Eq.  8l7  in  Eq.  4l9 

7  udu 

^~zt1/{a2-u2) 

4.  Substituting  values  of  y/(2ay — y*)  Eq.  ll9 

(a—y)  Eq.  8lf  and  dy  Eq.  41?  in  Eq.  1, 

7         n2du 
dx= 

a2 — u2 

5.  Integrating  Eq.  4,  x=  |     u 

J  a2 — u2 

u2  "2 

12.  By  division  .  =  —  1-j- 


or — vr 

az — uf 

2, 

Decomposing 

a2          A 
a2—u2     a — u 

a-\-u 

3.2. 

Reducing  to  common  denominator 
a2        Aa-f-  Au-\-Ba- 

-Bu 

a2 — u2 

a2 — u2 

4J.  Clearing  Eq.  32  of  fractions 

a8=(A+B)a-j-(A— ■ B)u 
52.  Transposing  Eq.  42  0=(A-fB)a+(A— B)w— a3 
62.  Eq.  42  being  true  for  all  values 

of  u,  is  true  when  u=0 ;  hence     A — B=0  ; 
72.  And  A+B=a 


96  QUARTZ    OPERATOR'S 

82.  Adding  Eqs.  62  and  72;    and  dividing  by  2,  A=  - 

Z 

92.  Subtracting  Eq.  63  from  Eq.  72;  dividing  by  2,  B=_ 

Z 

102.  Substituting  values  of  A  and  B 

a2  a  a 


in  Eq.  23 


a2  —  u2     2  (a  —  u)      2  (a  +  u) 

112.  Substituting  value  of 

a2      .    ^     -       u2  1  a  a 

in  Eq.  12 = — 1+- 


a2 — u2  a2 — u2  2  (a — u)    2  (a-\-u) 

6.  Substituting  value  of 

u2      .    w     -            C    j     x   C    adu       i   r    ^w 
in  Eq.  o ;  £==  |  — du-\-  1 -f-  I «, 

a2 — u"  J  J  2  (a — u)    J  2  (a-|-  u) 

When  #=0,  w=0  also  C=0  ; 

7.  hence,  #= — u — _7(a — w)-f--Z(a-|-#) 

8.  which  may  be  rendered      x== — u-\-^l  (  —£-  ) 

9.  Integrating  Eq.  2,     «—  f^  =— al{a— y)  +  C 

J a—y 

When  3/=0>  z=0  and  C=ala 


HAND    BOOK.  97 

10.  hence,  z—ala — at  {a — y) 

11.  which  may  be  rendered     z=al( ) 

\a~  y' 

Z,  in   the  above    calculations   denotes  the   Naperian 
logarithm. 

TO  FIND  THE  AREA  OF  THE  MERIDIAN  PLANE  COIN- 
CIDING WITH  THE  AXIS  OF  REVOLUTION  OF  THE 
TRACTORY    CONOID. 

(b)0.  Differential  Equation,  c?(area)  =ydx 

(b)v  Substituting  value  (dx)  Eq.  1;  ydx=\/  [2ay—yi)dy 
(5)3.  Putting  y=a — n;  ydx— — \/(a2 — n?)dn 
(b)3.  Decomposing  and  integrating, 

fydx^—Ccfia*—?!2)  ~  %dn+C?i2{a*—n2) "  %dn 
(5)4.  Second  term  of  Eq.  (b)5 ; 

CtficP—tf) "  %dn=—nl/  (a2  —  n*)+fdn  yV— r?) 

(b)5.  Substituting  in  Eq.  {b)s,  —C{a*-rfT$dn= 

^Ca%a2-nT^dn^n(a'^n^+C(a2^n^dn 
(5)6.  Transposing, 

E 


98  QUARTZ    OPERATOR'S 

(b)7.  But,  _  I  _— -=-^™s    (  -  ) 

(b)&.  Hence, 

-C(c?-n*fidn==^cos-  f7^ -^{cf-r?)  +  C 

(5)9.  Restoring  value  of  n,         I  -|/ \2ay~yi)dy  r= 

2  V    a    J        2 

Making  #=0;  Then  C=0. 

(b)10.  Uence,jl/(2ay—yi)dy= 

^cos-(aZiy\-J^V{2ay^) 
2  V    a    J        a 

(5)n.  Making  y=a.     Area=__    (0)=__^_==  _ 

(5)13.  Makingy=2a.  Area  =-^  cos"  (-1)=—  X-^=^-T 

4a 
Making  y=—<,  as  adopted  in  one  of  the  inventions 

of  Wheeler  &  Randall,  viz :  in  their  grinder  and  amal- 
gamator having  the  greater  base  of  its  muller  upward. 
Making  a  =1,  or  unity. 

Area   ==  lcos~  (,6)  —  ?(,8)=,2232  half  plane  of  muller. 
2  2 


HAND    BOOK.  99 

lence,  area  =,4464  entire  plane  of  muller. 
10    FIND    THE    SURFACE    OF    REVOLUTION    OF    THE 
TRACTORY    CONOID. 

(c)v  Differential  Equation  ^(surface)  =  (a — y)dz 
(c)3.  Substituting  value  of  dz  JEq.  2,  ds=2nady 
(c)3.  Integrating  s=2nay 

(c)4.  Making  y=a  s=2na2 

Making  y=,4,  as  adopted  in  that  grinder  and  amal- 
gamator of  Wheeler  &  Randall,  having  its  greater  base 
upward. 

(c)5.  Surface  of  revolution  =s=2,5028 

TO   FIND    THE   SOLID    CONTENTS    OF   THE    TRACTORY 

CONOID. 

Cj.  Differential  Equation,  d  (solid  contents) =n(a--yydx 

ez.  Substituting  val.  dx.  eq.  1, 

dC0=n(a^y)y/(2ay-y2)dy 

es.  Put  a~y=,n  then  y=a — n 

e4.  dC0= — iiai/ (a*-^n?)dn 

ds 
e5.  Put  s=dl — w2,    then  ds= — 2ndn,    and  — =  — ndn 

A 
€6.  Substituting  in  Eq.  e4       dC0=~ — - 


e7.  Integrating  Eq.  eQ  C0= 


e2 


100 


QUARTZ    OPERATOR'S 


e8.  Restoring  (a2 — ri2)  for  s,     C0=  — - — . L 


ed.  Restoring  (a~y)  for  n        C0  =  — — f"^  ' 

o 


e10.  Making  y=a 


n      lice 
C„=— 


en.  Making  y=J^==.  ,4  when  a=unity  C0=  ,5362 

10 
♦ 

The  following  table  is  computed  by  making  the  tan- 
gent a  —  1,  and  assigning  different  values  to  u,  not 
greater  than  a  as  shown  in  column  marked  u.  That  is, 
these  values  are  substituted  in  equations  8,  3  and  11, 
and  the  co-ordinate  values  of  x  and  y,  and  the  length  of 
the  tractory  curve  z,  thus  determined  in  terms  of  the 
tangent  or  unity  : 

TRACTORY    TABLE. 


a 

I 

:n;o 

u 
,100 

X 

y    r  z    \ 

,00501 4!005027 

No 
14 

u 

x            y 

z 

i 

,000336 

,725 

193102311251 

368505 

2 

,150 

,001136 

,011316011379 

15 

,750 

222956338562 

413293 

3 

,200 

,002732 

,020205  029412 

16 

,775 

2577301368039 

458928 

4 

,250 

,005415 

,031756  032260 

!7 

,800 

298611  400000 

510827 

5 

,300 

,009514 

,046063j047157 

18 

,825 

347276434867 

570796 

6 

,350 

,015454 

,063252  065571 

19 

,850 

406153  473297 

641118 

7 

,400 

,023648 

,0834851087178 

20 

,875 

479027.515878 

725418 

8 

,450 

,034699 

,106972  113137 

21 

,900 

572220564109 

830367 

9 

,500 

,049304 

,133976  143842 

22 

,925 

697603620033 

967651 

10 

.550 

,068381 

,164835:180127 

23 

,950 

881785687751  1,163903 

11 

,600 

,093146 

,200000l223144 

24 

,975 

1,209723  777795  1,504152 

12 

,650 

,125296 

,240065  274523 

25 

,99011,656677  858933  1,958518 

13 

,700 

,167304 

,285857'336672 

26 

,999*2,801 193  955289  3,107543 

HAND  BOOK. 


101 


TO  CONSTRUCT  THE  TRACTORY  BY  THE  PRECEDING 
TABLE. 

Draw ,  the  rectangular  co-ordinate  axes  AX,  AY, 
Figure  2. 

On  AY,  lay  off  AF,  equal  to  the  given  tangent,  and 
draw  the  directrix  FD,  parallel  with  the  axis  AX, 
through  the  point  F. 


f;3.2. 


Multiply   any   tabular 

A.  quantity  in  column  x  by  the 
B    given  tangent,  and  lay  off 

B,  the  product  as  AB  or  AX. 
„  Draw  BE  parallel  with  AF. 
,„      Multiply  the  quantity  in 

column  y,  horizontal  with 
the  quantity  taken  in  column 
x,  by  the  given  tangent,  and 
lay  off  the  product  as  BC  on 
the  line  BE.  The  point  C 
is  in  the  curve. 


In  a  similar  manner  determine  the  points  C,  C",  C", 
C"",  etc.,  etc.,  in  the  curve. 

Multiply  the  quantity  in  column  z  horizontal  with  the 
quantities  thus  taken  in  column  x  and  y,  and  the  pro- 
duct will   be   the   length   of   the  curve  A  C,  A  C  C, 

etc.,  etc. 

e3 


Y 

F 

E 

(?/ 

£' 

.z___ 

J?" 

C7 

E!r 

/ 

can 

M 

rrm 

I 

1 

102  QUARTZ    OPERATOR'S 

When  the  points  A,  C,  C,  C",  C",  etc.,  are  not  far 
apart,  the  arc  of  a  circle  drawn  through  any  three  of 
them  taken  consecutively,  approximates  the  true  curve 
sufficiently  near  for  most  practical  purposes.    ; . 

Ex. — Let  it  be  required  to  find  the  values  of  x',  y\ 
and  z',  when  the  tangent  a  =  24  for  the  point  C. 

Now  since  C  may  be  any  point  of  the  curve,  let  the 
co-ordinate  x  be  taken  in  the  table  opposite  No.  17. 

Then,  2±x  =  A B'  =24  X  ,298611  =  7.166664=^ 
24  y  =  B'  C  =24  X  ,400000  =  9.600000  =y' 
24  z  =  ACC  =24  X  ,570827  =12.259848  =*£ 

Laws  of  Grinding. — 1.  The  measure  of  a  unit  of 
grinding  effect  is  the  "result  of  a  body  impressing  a  unit 
surface  of  another  body  with  a  unite  pressure,  and 
moving  over  a  unite  space. 

2.  A  body  impressing  a  unite  surface  of  another  body 
with  a  unite  pressure,  and  moving  under  these  circum- 
stances over  a  unite  space,  producing  thereby  a  uniie  of 
grinding  effect,  (the  pressure  being  uniform  and  the 
nature  of  the  surfaces  of  contact  being  the  same)  pro- 
duces as  many  units  of  effect  as  there  are  units  in  the 
distance  passed  over. 

3.  The  wear  or  distinction  to  the  moving  body  per- 
pendicular to  the  surfaces  of  contact,  bears  a  constant 
ratio  to  the  distance  passed  over. 


HAND   BOOK. 


103 


MS.3. 


To  prove  that  to  grinding  plates  coinciding,  of  uniform 
hardness,  and  of  tractory  conoidal  form,  the  wear  paral- 
lel with  the  axis  of  revolution  is  the  same  at  all  points  of 
the  grinding  surface. 

Let  A  F  D"  C"  represent  one 
half  of  a  meridian  plane  of  a 
tractory  conoid  taken  through 
the  axis  or  directrix  F  D". 

Draw  C  D  =■.  a,  and  C  D' 
=  a  each  tangent  to  the  curve 
at  any  points  C,  C  ;  also  draw 
the  radii  CE  =  r  and  C  E'  = 
r'  parallel  with  A  F. 

Let  w  =  o  c  denote  the  wear 
perpendicular  to  C  D,  and  wf  = 
o'  cf  the  wear  perpendicular  to 
C  D'. 

Let  P  =  C  c  and  P'  =  C  c  denote  the  wear  re- 
spectively at  the  points  C,  C  and  each  parallel  with  the 
axis  F  D". 


h- 

Then  by  law  2d, 

w'  = 

HU  T 

r 

2s. 

By  similar  triangles, 

P  = 

a  w 
r 

33. 

By  similar  triangles, 

P'  = 

awf 

e4 


104  QUARTZ    OPERATOR'S 

42.  Substituting  value  of  wK  Eq.  13 

a  w  r1 
in  Eq.  33  P  =  -^r- 

53.  Reducing  2d  member  of  Eq.  43    P'  =  — 

63.  Substituting  value  of  —  in  Eq.  23   P'  =P 
73.  That  is,  C'c'  =  Cc 

(a)  Hence,  as  the  wear  is  the  same  at  any  two  points 
as  shown-  by  Eqs.  63  and  73,  it  is  the  same  at  all  points 
parallel  with  the  axis,  of  revolution. 

(b)  And  hence  the  curve  A'  c  c'  c"  is  similar  and 
equal  to  the  tractory  ACC  C". 

Again,  plates  whose  grinding  surfaces  are  of  tractory 
conoidal  form,  alone  passes  the  property  of  uniform  wear 
parallel  with  the  axis  of  revolution. 

To  prove  this  proposition 
Put  (Fig.  3)  a'  =  C  D' 

83.  Then  Eq.  53  becomes  P'  = 

r 

93.  From  Eq.  23  and  83  we  have     P :  P' : :  — :  — 

r       r 

103.  Reducing  2d  couplet  P :  P' :  :  a  :  af 

Proportion  103  shows  that  the  wear  P  is  equal  to  P' 
only  when  tangent  a  is  equal  to  d  ;  but  when  a  is  equal 
to  a!  the  line  or  curve  is  a  tractory.  Q.  E.  D. 


HAND  BOOK. 


105 


TO  DETERMINE  THE  SOLIDITY  OF  A  HOLLOW 
TRACTORY  CONOID. 


Jfy.4* 


J>              &'G' 

e      a. 

Jj 

I . 

L        C 

'           AL 

JS> 

I' 

.A 

V 

C"l 

/  / 

J) 

A 

C" 

I r" 

r 

Let  AFD'C"  represent  one- 
half  of  a  meridian  plane  taken 
through  the  axis  F  D'. 

Draw  the  curve  A'  c  c'  c"  c'" 
similar  and  equal  to  the  tractory 
ACC  C"  C",  and  at  the  dis- 
tance A  A',  C"  c"  from  it.  (See 
conclusion  {b). 

Draw  A'EjC'E^E",  par- 
allel with  A  F,  also  G  c  through 
C,  GV,  through  C,  G'V,  thro- 
ugh C"  parallel  with  F  D'. 
Since  the  curve  c' c"  is  similar 
and  equal  to  C  C",  and  the  line  C  c'  =-  C"  c",  and  C  I' 
=  c'C",  and  the  angle  c'C"c"=the  angle  CTC"; 
it  follows  that  the  triangle  c"  c'  C"=  C"  C  I',  and  also 
similar  to  it. 

And  since  the  conoidal  triangle  C"  c'  C  is  common  to 
the  parallelogram  C"  c'  C V,  and  to  the  conoidal  section 
c"  c'  C  C",  it  follows  that  the  conoidal  section  c" V  C  C" 
is  equal  to  the  parallelogram  C"  c'  C I'. 

Again,  since  c'C'  =  A/A  =  LG',  and  C"c  =  IL, 
it  follows  that  the  parallelogram  c'V  =  the  parallelo- 
gram L  G".  Hence  the  conoidal  section  c"  c'  C  C"  = 
the  parallelogram  L  G" ;   and  since  its  position,  in  all 

respects,  is  at  the  same  distance  from  the  axis  F  D',  it 

s5 


106  QUARTZ    OPERATOR'S 

is  evident,  if  it  be  revolved  about  F  D'  as  an  axis,  it 
will  generate  a  conoidal  ring  of  the  same  magnitude  as 
a  ring  generated  by  revolving  L  G"  about  the  same 
axis. 

In  the  same  manner  may  it  be  shown  that  any  oo- 
noidal  ring,  under  similar  circumstances,  is  equal  to  the 
ring  generated  by  revolving  the  corresponding  paral- 
lelogram taken  in  ^AFE  around  the  axis  F  D'. 

Hence  the  solidity  of  a  hollow  tractory  conoidal  is 
equal  to  the  solidity  of  a  cylinder  having  the  same  base 
and  same  height  as  A'  A,  c"  C",  measured  parallel  with 
the  axis  of  revolution. 

Tractory  Plates, — To  determine  the  grinding  effect  of 
hollow  tractory  conoidal  plates  of  uniform  hardness. 

Let,  as  in  Figs.  1  and  2,  the  tangent  or  greater 
radius  sss  a. 

Let  x  and  y  be  co-ordinates  of  any  point,  C,  etc. 

Let  z  denote  the  length  of  curve  A  C,  etc. 

Let  P  denote  the  wear  parallel  with  the  axis  of  revo- 
lution, by  one  revolution  under  a  unit  pressure  to  a  unit 
surface.  » 

Let  S  denote  the  grinding  surface. 

Let  ii  denote  the  ratio  of  the  diameter  to  the  circum- 
ference of  a  circle. 
14.  Then,  d$  =  2n(a—  y)dz 

24.  Substituting  value  of  dz  of  Eq.  2, 
io  Eq.  1^  da  »  2uady 


HAND    BOOK.  107 

34.  Then,  by  one  revolution, 

2nP(a  —  y)ds  b  4n2Pa2<fy  —  An2Faydy 
44.  Integrating  Eq.  34, 

2nP(a— y)ds  =  4n2Pa#  —  %ii2Patf 

54.  Resolving  2d  member  of  Eq.  44  into  factors  ; 

f2nP(a  —  y)ds  =  2n8Pa(2ay  —  f) 


i> 


s* 


64.  By  making  y  =  a  in  Eq.  54 ; 

Grinding  effect  =  2n2Pa3 

Plane  Plates. — To  determine  the  grinding  effect  of 
plane  circular  plates,  increasing  in  hardness  from  the 
center  to  the  circumference  in  the  ratio  of  the  increase 
of  the  radius. 

Let  a  =ss=  the  radius  of  the  plates. 

Let  y  =  any  radius  of  the  plates  less  than  a. 

Let  P  =  the  wear  at  the  circumference,  perpendicular 
to  the  grinding  surface,  under  a  unit  pressure  to  the 
unit  surface,  by  one  revolution. 

Let  ii  =  ratio  of  diameter  to  the  circumference  of  a 
circle. 

15.  Then  ds  =  2nydy 

25.  By  one  revolution,  2liPyds  =  4ii2P^ dy 

S5.  Integrating  Eq.  25,  f  2nPycfe  =  -  n*Ff 

J  3 

45.  By  making  y  =  a  in  Eq.  35 ; 


Grinding  effect  =  -  n2Pa8 
3 


sC 


108  QUARTZ    OPERATOR'S 

Plane  Plates. — To  determine  the  grinding  effect  of 
plane  circular  plates  of  uniform  hardness. 

Let  a  ==s  the  radius  of  the  plates. 

Let  y  —  any  radius  less  than  a. 

Let  P  ===  the  tendency  to  wear  at  the  circumference, 
perpendicular  to  the  grinding  surfaces. 

Let  S  =  the  surface  of  which  y  is  the  radius. 

Let  ii  ==  ratio,  etc. 
16.  Then  ds  =  2  n  y  dy 

Now,  it  is  evident  that  when  the  tendency  to  wear  at 
the  circumference  and  at  the  distance  a  is  P,  that  the 
tendency  to  wear  at  the  distance  y  from  the   centre 

will  be  5? 

26.  Then  by  one  revolution  2ll^yds  =  4n2p^ 

a  a 

36.  Integrating  Eq.  26  fl^yds  =  *5-3?1 

46.  Reducing  2d  member  of  Eq.  36  — ; 


p 


.yds 


a 


5e.  By  making  y  =  a  in  Eq.  46, 

Grinding  effect  =  n2Pa8 

Conical  Plates. — To  determine  the  grinding  effect  of 
hollow  conical  plates  of  uniform  hardness. 


J3AND    BOOK. 


109 


Fig.  5. 


Let,  in  Fig.  5,  the  right  angled 

triangles  ABC  and   A'  B'  C> 

similar  and   equal,  and   at   the 

A'  distance  AA'  =  CC  apart,  be 

revolved  about  the  axis  B  C 

Then  will  the  solid  generated 

by  A  A'  B  B'  be  equal  to  the 

solid    generated  by  C  A'  A  O 

Let  a  —  the  radius  B  A. 

Let    h    tsz    height    of    cone 

BC=B'  C.  % 

Let  P  =  tendency  to  wear  at 
A,  parallel  with  the  axis  of  rev- 
olution, by  one  revolution  of  the  plate  under  a  unit 
pressure  to  a  unit  surface. 

Let  x  and  y  be  co-ordinates  of  any  point  P. 
Let  z   =    C  P  the  slant  height  of  that   cone   the 
radius  of  whose  base  is  y. 

Let  S  =  the  surface  whose  slant  height  is  z. 
Let  ii  =  ratio,  etc. 


17.  Then  by  similar  triangles 


hy 


%.  And  (Euclid,  Book  1,  Prop.  47)    ar2  +  y2  =  z> 

37.  Squaring  Eq.  17  x2  rz  —JL 

a 

4j.  Substituting  value  of  x2  of  Eq.  37  in  Eq.  27 


110  QUARTZ    OPERATOR'S 

57.  Extracting  square  root  of  Eq.  47 

67.  Surface  of  cone  whose  slant  height  is  z 

77.  Differentiating  Eq.  610  ds  =  2  n  -j/  fE  +  l\y  dy 

When  the   tendency  to  wear  at  A  is  P,  it  is  evident 
that  the  tendency  to  wear  at  P  is      ^  parallel  with  the 


axis. 

87.  Hence  differential  of  effect 


1±U?  ds  =  t2L*jL{»+  l\  f  dy 

a  a         \a2        y 

97.  Integrating   Eq.   87    ClllE^ds=  l£E(£  +  l)y* 

107.  By  making^  —  a  in  Eq.  97. 

Grinding  effect  =  n2  P  \/f-;  +  l^a3 

117.  By  making  h  =_  in  Eq.  107. 

Grinding  effect  =  1L_  i/o" 
2       Y 

12^  Removing  surd  sign  from  2d  member  of 

Eq.  llr.     Grinding  effect  «  1.118  ll9  P  a8 


HAND    BOOK.  Ill 

Comparison. — Let  a  comparison  now  be  instituted 
between  the  grinding  effects  of  plane  circular  plates,  in- 
creasing in  hardness  from  the  center  to  the  circumfer- 
ence in  the  ratio  of  the  increase  of  the  radius,  plane 
circular  plates  of  uniform  hardness,  "  Randall's  Patent 
Grinding  Plates,"  conical  plates  of  uniform  hardness, 
and  tractory  conoidal  plates,  and  all  of  the  usual  ring, 
form,  same  diameter,  same  weight,  and  running  at  the 
same  velocity. 

1st.  Plane  circular  plates,  increasing  in  hardness  from 
the  center  to  the  circumference  in  the  ratio  of  the  in- 
crease of  the  diameter. 

Making  y  less  than  a.     For  example,  y  =  J  and 

o 

substituting  this  value  for  y  in  Eq.  35,  and  we  have 


18.  Grinding   effect  (the  radius  being  f)=  J-ii2Pa3 

O  Li 


sinS  ->)  = 
o 

28.  Subtracting  Eq.  18  from  Eq.  45. 

32 

Grinding  effect  (ring)  =  —  irPa8 

38.  Or  expressing  decimally. 

Grinding  effect  (ring)  ==  1,1852  II2  P  a3 
2d.  Plane  Circular  Plates  of  uniform  hardness. 

Making  y  less  than  a.     For  example,  y  =  a'  and 

o 

substituting  this  value   for  y  in  Eq.  46,  and  we  have 


19.  grinding  effect  (radius  being  2_) 


ii3  P  a3 


8  81 


112  QUARTZ    OPERATOR'S 

29.  Subtracting  Eq.  19  from  Eq.  56, 

n  .    ,.        ~    l,  . .     v       80  ii2  P  a3 
Grinding  enect  ( ring)  = 

.  81 

39.  Or  expressing  decimally. 

Grinding  effect  (ring)  ==  ,9877  n2  P  a3 

3d.  Randall's  Patent  Grinding  Plates. — These  plates 
consist  of  two  or  more  concentric  rings  of  different  hard- 
ness. The  softer  plates  are  arranged  nearer  the  center 
where  there  is  the  less  wear,  and  the  harder  plates  more 
remote  where  the  wear  is  greater.  This  arrangement 
remedies  in  a  great  measure  the  otherwise  fatal  defects 
of  plane  circular  and  conical  plates. 

For  Example. — Let  a  =  the  greater  radius  of  the 
plates. 

Let  -  rr  the  radius  of  the  opening. 

2a 
Let    —  the  greater  radius  of  the  inner  ring. 

3 

1st.  Making  y=-,  and  substituting  this  value  for  y 
o 

in  Eq.  46,  and  we  have 

n2Pa3 


110.  Grinding  effect  (  radius  -  j 


81 


v  2a 

2d.  Making  y  ■zz  — ,  and  substituting  this  value  for 

y  in  Eq.  46,  and  we  have 

210.  Grinding  effect  (  radius  -q)  —  — ^r — 


HAND    BOOK.  113 


310.  Subtracting  Eq.  110  from  Eq.  56; 

80 
Grinding  effect  (ring)  ^  —  n2Pa3 
V      oJ       81 

4i0.  Subtracting  Eq.  210  from  Eq.  56 

Grinding  effect  (ring)  =  -  u2Pas 

510.  Comparative  weight  of  the  outer  ring, 
2_4a2=5^2 
9        T 

610.  Comparative  weight  of  entire  plane,  less  the  opening, 

.3__  a2^^2 

9"      ~9~ 

-      rp,                5a2.   8a2       65n3Po8     104n2Pa3 
710.   Inen  :  :  : : 

9         9  81  81 

8io-  Or  grinding  effect  of  outer  ring,  =  —  n2Pa3 

81 

910.  The  loss  sustained  by  plates  of  uniform  hardness, 

104*  2t>  .       80    9n,       24    ,„  o 

== n2Pa3  —  _  n2Pa3  =  _  n2Pa2 

81  81  81 

Let  it  now  be  assumed  that  the  inner  plates  or  rings 
are  one-third  as  hard  as  the  outer  plates. 
1010.  See  Eq.  910.     Loss  sustained, 

81  81 


114  QUARTZ    OPERATOR'S 

Subtracting  Eq.  1010  from  Eq.  810,  gives  for  "RandaWs 
Patent  Grinding  Plates,  viz, : 

Grinding  effect  =  . 

81 
1 210.  Expressing  decimally  ; 

Grinding  effect  =  1.1852ii2P«3. 
Subtracting  Eq.  29  from  Eq.  1110,  and  dividing  the 
remainder  by  Eq.  29,  gives  the  per  centage  of  "  Ran- 
dall's Patent  Grinding  Plates,"  both  over  plane  circular, 
and  conical  plates  of  uniform  hardness,  as  follows : 
1310.  Per  centage  in  favor  of  "  Randall's  Patent  Grind- 

ing  Plates,"  ( 96 nW  __80ii W)  £_81_        2Q 
v      81  81      J        80n2Pa3 

4th.    Conical   Plates   of    uniform    hardness    and   of 
ring  form. 

ln.  Making  y  less  than  a,  for  example  y=-,  and  substi- 

o 

tuting  this  value  for  y  in  Eq.  97,  and  we  have  the  grind- 
ing effect  ("the  radius  °L\  =  ^^f  *L+  1  ^S 

2n.  Subtracting  Eq.  ln  from  Eq.  107. 

n  -    v        t   *  f  -     \     80n*Pa3  ,>#    .     ,\ 
Grinding  effect  (ring) = j/(  — -p   1    J 

8 1  V«2  J 

3U.  Making  h  =,"  in  Eq.  2n. 

Grinding  effect  (ring)  =  Sln2F aYf-^) 
81  v4>/ 


HAND    BOOK.  .115 

4n    Expressing  decimally. 

Grinding  effect  (ring)  =  1,1042  n2  P  as 

5th.   Tractory  Conoidal  Plates  of  uniform  hardness. 

2  a 
Making  y  less  than  a.     For  example  y  =  —'as  is 

5 

the  case  in  the  Wheeler  &  Randall  muller   or  grinding 

plates. 

2  a 
112.  Substituting .  for  y  in  Eq.  54. 

5 

„.        „    .        32n2Pa3 

Kino;  effect  = J 

25 

212.  Making  the  tractory  conoidal  plate  of  the  same 
weight  or  solidity  as  the  plane  circular  or  conical  plates, 

and  Eq.  113  becomes  Grinding  effect  (ring)  =  —  if  P  a5 

312.  Expressing  decimally. 

Grinding  effect  =  1,7778  n2  P  a3 

Recapitulation. — To  express  the  relative  grinding 
effects  of*  the  differently  formed  plates  now  considered, 
the  literal  factors  n2P  a3,  common  to  all  their  formulas, 
may  be  omitted. 

Omitting  the  literal  factors,  and  the  relative  grinding 
effects  of  differently  formed  plates  become  as  follows,  to 
wit : 

ll3.  Eq.  39. — Plane  circular  plates  of  uniform 
hardness  =  ,9877. 


116  QUARTZ    OPERATOR'S 

2,  3.  Eq.  1210. — Randall's  Patent  Grinding  Plates 
=  1,1752. 

313.  Eq.  41]L, — Conical  plates  of  uniform  hardness 
=  1,1042. 

4l3.  Eq.  312. — T ractor j  conoid al  plates  of  uniform 
hardness  ==  1,7778. 

Hence  the  conclusion  that  tractory  conoidal  plates  not 
only  differ  materially  in  form  from  plane  circular  and 
from  conical  plates,  but  also  differ  essentially  from,  and 
are  greatly  superior  to  them  in  their  grinding  properties. 


HAND  BOOK. 


117 


PRORERTIES  OP  BODIES. 


NAME. 

Specific   Melt'ng  Rates 
gravity     points   of'h'rd- 
at  ;J2Q  f  h.  at  fahr.    nes s . 

Tenacity 
in  lbs.  per 
sqr.  inch. 

Crush'ng 
force  in 
Ibs.sq.  in 

Volatile  at 

20.336  3^80° 

very  high  ht. 
very  high  ht. 

do  drawn  wire 

21.042 
22.069 
19.258 
19.361 

34000 

do    plates .... 

Gold,  cast 

do  liammered. 

2016 

1.8 

18000 

moderate  ht. 

do   wire 

28000 
36000 

Silver,  cast. . .  . 
do    hammered 

10.474 
10.510 

1873 

2.4 

high  heat. 
high  heat. 

do   wire 

34000 
17000 
30000  ( 
42000  \ 
55000 
4000 

117000 

92000 

103000 

high  heat, 
high  heat. 

>  high  heat. 

Copper,  cast. .  . 
do    hammered 

8.788 
8.910 

1996 

2.8 

do    sheets  .  . . 

do    wire 

Tin,  cast 

do    hardened . 

7.291 
7.291 

442 

1.2 

15500 

do    wire 

6000 

Zinc,  cast 

6.200 

7.191 

11.352 

773 

1.6 

white  heat. 

do   sheets 

Lead,  cast 

1600 
3000 
2200 

7730 

white  heat. 

do  milled. . . . 

do    wire 

Mercury 

Iron,  cast,  gray. 
do    do   white. 

13.598 

7.248 
7.500 
7.788 

I 

—39 
2800 

680° 

any 
deg. 

4.7 

j 

very  high  ht. 

do  forged .... 
do    wire,  1-20 

120000  1 
182000  \ 
72000  ) 
86000  J 

54000 



to  1-30  in.  diam 
Iron,  wire,  1-10 
inch  diameter.. 
Iron  bars,  Rus- 

i 

\ 

\ 

sian,  mean 

Iron,  American 

gun  metal 

Iron,  American 
gun  motal.mean 
Iron.      English 

Stirling 

Iron,      English 
Stirling,  mean. . 

\ 

147803 

129000 

119550 

90833 

I 

I 

1 

s 

f 

118 


QUAl'iTZ    OPERATORS 


PROPERTIES 

OF 

BODIES. — CONTINUED. 

NAME. 

Specific 
gravity 
at  32°  f'h. 

M*H'ng  Rntes 
points   ofh'ru- 
at  fahr.    ness. 

Tenacity    Crush'ng 
in  libs,  per    force  in 
sqr   inch,    lbs  sq,  in 

Volatile  at 

Iron,  American 

1 

.    .... 

83500 

65200 

198944 

373041 

295000 

wrought,  mean. 
Iron,     English, 

1 

wrought,  mean. 
Steel,    cast,     ) 

soft S 

Steel,   cast,     1 
tempered. . . .  ) 
Steel,    cast,     ) 
tern  p'd,  mean  ) 

) 

7.833 
7.816 

88000 

17.600 
7.824 

155916 

146000 
164800 

1900c 

16000 

8.396 

Nickel,  cast. .. . 

8.279 
9.880 
6.702 
5.763 
8.600 
8.600 

2.716 

2810 
476 
932 
400 

very  high  ht. 
white  heat. 

Bismith 

2.0 

Antimony 

Arsenic ....... 

white  heat. 

356° 

Cob 'It 

very  high  ht. 
600° 

550 

Stone,   mar-   \ 
blc,  white . . .  ) 
* Stone,  marble 

8000 

2800 
10382 
23917 
22702 
12624 
11200 

5340 

3319 
3065 

Stockbridgg. . . 
t  Stone,  marble 

J 
1 

East  Chester  . . 
Stone,    marble, 

) 
\ 

Lee,  Mass 

Stone,   marble, 

) 
\ 

Italian 

Granite,  Pa-   ) 

tapsco ) 

t  Sand  Stone,  / 
Aquia  Creek.  ) 
Freestone,  Con. 

) 

2.613 

2.956 

i 

s 

Limes! one  .... 

2 .  386 

♦Same  as  that  of  Ciiy  Mall,  Mow  York, 
f  Same  as  that  of  General  Post  Office.  VVashington. 
%  Same  as  that  of  tho  Capitol,  Treasury  Department,  and  Post  Office 
Department,  D.  O. 


HAND    BOOK. 


119 


PROPRTIES  OF   BODIES — CONTINUED. 


NAME, 

Specific 
gravity 
at  328  fh. 

Melt'ng 
points 
at  fahr. 

Rates 
ofhr'd- 
ness. 

Tenacity 
in  lbs.  per 
sqr,  inch. 

Crush'ng 
force  in 
lbs.  sq.  in 

Volatile  at 

Mica. 

2.650 

Quartz <j 

Serpentine 

Cinnabar  

2.624 
3.75U 
2.264 
6.902 
2.438 
2.582 
.845 

[ 

) 

Felspar 

Flint 

Ash 

8663 
4100 
5982 
6484 
5375 
6645 
5768 
10331 

Oak,  American 

do    Canadian. 

do  English.. . 

.920 

Pine,  Yellow.  . 

Walnut 

Cedar  

Kim 

.671 
.600 
.862 

12000 
10000 
18000 

Fir 

Box 

Teak 

12100 

120  QUARTZ    OPERATOR'S 

MISCELLANEOUS. 

5760  grains  =  1  pound  troy  =  1  pound  apothecary. 
480  grains  =  1  ounce  troy  =  1  ounce  apothecary. 
1 2  ounces  =  1  pound  troy  =  1  pound  apothecary. 
7000  grains  =  1  pound  avoirdupois. 
437,5  grains  =  1  ounce  avoirdupois. 
1 6  ounces  avoirdupois  =  1  pound  avoirdupois. 
252,458  grains  =  1  cubic  inch  distilled  water,  Eng- 
lish standard  62°  Fahr.,  Barometer  at  30  inches. 

252,693  grains  =  1  cubic  inch  distilled  water,  U.  S. 
standard  30.83°  Fahr.,  Barometer  at  30  inches. 

27,7015    cubic   inches   distilled   water  =   1    pound 
avoirdupois. 

1  cubic  foot  distilled  =  62,37929  pounds  avoirdupois. 
321  cubic  inches  =  8,3388822  pounds  avoirdupois  = 
1  gallon  U.  S. 

277,274  cubic  inches  =  10  pounds  avoirdupois  =  1 
gallon  Imperial. 

2150.42  cubic  inches  =77,627413  pounds  avoirdupois 
=  1  bushel. 

1  grain  Gold,  1000  fine  =  $,0430663  Mint  value. 
1  grain  Silver,  1000  fine  =  ,0026936  Mint  value. 
1  grain  Copper,  1000  fine  =  ,0000595  Mint  value. 
1  ounce  Gold,  1000  fine  =  20,671791  Mint  value. 
1  ounce  Silver,  1000  fine  =  1,292929  Mint  value. 
1  ounce  Copper,l 000  fine  =  ,028571  Mint  value. 
23.22  grains  Gold,  1000  fine  +  2.58  grains  alloy  = 
25.8  grains  =  $1.00. 


HAND    BOOK.  121 

371.25  grains  Silver,  1000  fine  +  41.25  grains  alloy 
=  412.5  grains  =  $1.00. 

16800  grains  Copper,  1000  fine  =  $1.00. 

1  cubic  inch  Gold,  1000  fine  =  10,12883  ounces  troy 
=  $209.38. 

1  cubic  inch  Silver,  1000  fine  =  5,50885  ounces  troy 
=  $7.13. 

1  cubic  inch  Copper,  1000  fine  =  4,62209  ounces  troy 
=  $0,133. 

Gold  and  Silver,  when  pure,  are  said  to  be  1000  fine ; 
or,  by  the  old  method,  24  carats  fine. 

The  standard  fineness  of  the  United  States  Coin  is 
900  ;  or,  by  the  old  method,  24X,900  =  21.6  carats  fine. 

gunter's  CHAIN, 

7.92  inches  =1  link. 
100  links  =  4  rods  =  1  chain. 
5280  feet  =320  rods  =80  chains  =  1  mile. 
69.77  statute  miles  =  1  degree  of  a  great  circle  of  the 
earth. 

160  square  rods  =  10  square  chains  =1  acre. 
640  acres  =  1  square  mile. 

FRENCH  WEIGHTS   AND   MEASURES. 

1  Metre  =39.371  inches. 
1  Are  =3.953  square  rods. 
1  Litre  =  61.028  cubic  inches. 
1  Stere  =35,31714  cubic  feet. 
1  Gramme  =  15,434  grains  troy. 


122  QUARTZ    OPERATOR'S 

The  Greek  prefixes  Deca,  Hecto9  Chilo,  and  Myria, 
respectively,  signify  10  times,  100  times,  1000  times, 
and  10000  times. 

And  the  Latin  prefexes  Deci,  Centi,  and  Milli,  re- 
spectively, 10th  part,  100th  part,  and  1000th  part. 

Thus,  1  Deca-metre  =  10  metres,  and  1  metre  =10 
Deci-meters. 

Thus,  1  Chilo-gramme  =1000  grammes,  etc. 
1  Arroba  (Mexican)  =  26  pounds  avoirdupois. 
1   Fanega  =  1,599  bushels,  U.  S.,  =3438.52   cubic 
inches. 

1  Marc  or  Marco  =  8  ounces  troy. 
1  Vara  =  33,384  inches. 
25  cubic  feet  of  sand  =  1  ton. 
18  cubic  feet  of  earth  =  1  ton. 

17  cubic  feet  of  clay  =1  ton. 

13  -cubic  feet  of  quartz,  unbroken  in  lode,  =1  ton. 

18  cubic  feet  of  gravel  or  earth,  before  digging,  =27 
cubic  feet  when  dug. 

20  cubic  feet  of  quartz,  broken,  (of  ordinary  fineness) 
=  1  ton,  contract  measurement. 


HAND    BOOK.  123 

Oakland,  August  27,  1864. 

Mr.  Randall — Sir  : — I  have  carefully  examined  your 
demonstration  of  the  Tractory  Curve,  and  of  the  grind- 
ing effects  of  differently  formed  plates,  and  find  your 
calculations  correct. 

Yours,  etc.,  Francis  D.  Hodgson, 

Prof.  Math.  College  of  California. 


San  Francisco,  September  7,  1864. 

Mr.  M.  P.  Randall — Dear  Sir  : — I  have  to  thank 
you  for  the  opportunity  of  inspecting  the  drawing  and 
model  of  your  and  Mr.  Wheeler's  new  form  of  grinding 
and  amalgamating  apparatus,  in  which  you  have  adopted 
the  Tractory  Conoid  as  the  form  of  the  grinding  surfaces. 

Your  mathematical  demonstration  of  the  mechanical 
properties  of  this  curve  is,  so  far  as  I  am  informed, 
original  and  very  interesting,  and  satisfies  perfectly  the 
practical  requirements  of  the  problem.  The  Tractory 
Conoid  is  a  solid  the  nature  of  whose  curve  is  as  differ- 
ent from  that  of  the  surface  of  a  cone  as  is  a  cycloid  from 
an  inclined  plane. 

Your  mathematical  analysis  of  the  problem  of  uniform 
grinding,  by  tractoroidal  surfaces,  is  extremely  interest- 
ing, and  furnishes  a  fine  illustration  of  the  value  of  this 
method  of  discussion  applied  to  a  case  which  at  first  sight 

f2 


124  QUARTZ    OPERATOR'S 

would  seem  to  be  completely  beyond  the  reach  of  such 
subtle  and  exact  tests.  The  practical  value  of  this  dis- 
cussion and  of  the  results  which  it  appears  to  sustain,  are 
such  as  commend  it  to  the  serious  attention  of  all  who 
are  interested  in  the  development  of  the  resources  of 
the  Pacific  coast  in  the  precious  metals. 
Yours,  respectfully, 

B.  SlLLIMAN,  Jr. 


San  Francisco,  May  4,  1865. 

Gentlemen  : — Having  made  a  careful  and  critical 
examination  of  your  "  Quartz  Operator's  Hand  Book," 
it  is  with  extreme  pleasure  that  I  certify  to  the  correct- 
ness of  your  statements  and  deductions.  It  bears  the 
impress  of  extensive  research  and  thorough  investiga- 
tion. Your  discussions  of  all  the  various  subjects  are 
remarkably  clear,  concise  and  rigidly  exact ;  but  permit 
me  more  especially  to  congratulate  you  upon  your 
masterly  discussion  jof  the  Tractory  and  the  grinding 
effects  of  differently  formed  plates — a  subject  practically 
of  the  highest  importance  to  every  quartz  miner. 

With  sentiments  of  high  regard,  I  remain, 
Yours,  truly, 

W.  R.  Eckart,  Jr., 
Engineer  (late  of)  U.  S.  N. 

To  Messrs.  Wheeler  6?  Randall. 


HAND    BOOK.  125 

San  Francisco,  May  29,  1865. 

Messrs.  Wheeler  Sf  Randall : — Having  examined  your 
"  Quartz  Operator's  Hand  Book,"  I  take  pleasure  in 
recommending  it  to  miners  and  millmen,  as  a  work  likely 
to  be  of  great  use  in  properly  understanding  the  nature 
of  their  ores,  and  consequently  the  treatment  necessary 
to  produce  favorable  results. 

Respectfully,  yours,  etc., 

W.  M.  Belshaw, 

Assayer,  and  Sup't,  of  the  S.  T.  M.  Co. 


f3 


INDEX. 


Assay, 13 

Assay  Blowpipe, 4 

Assay  of  Copper — dry  way, 14-1 5 

Assay  of  Copper — humid  way, 17 

Assay  of  Gallena — dry  way, 14 

Assay  of  Gallena — humid  way, 17 

Assay  of  Gold — dry  way, 16 

Af say  of  Gold — humid  way 18 

Assay  of  Iron — dry  way, 14 

Assay  of  Iron  Ores  containing  Manganese, 19 

Assay  of  Silver — dry  way 16 

Assay  of  Silver — humid  way 17 

Assay  or  Analysis  of  Ores  containing  Gold,  Silver,  Copper, 

Lead,  Iron,  and  Sulphur, 20 

Blowpipe, 4 

Cupellation, 38 

Comparison, Ill 

Cement,  Iron  Rust, 22 

Chemical  Recipes, 84-35 

Chemical  Terms,  Explanation  of, 12 

Discussion  of  the  Tractory  and  differently  formed  Grinding 

Plates, 92-1 16 

f4 


128 


Evolution, 87 

Extraction  of  Gold  by  Chloration, 28 

Extraction  of  Gold  b j  the  Pan  Process, 26 

Extraction  of  Silver  by  the  Pan  Process 32 

Extraction  of  Silver  by  the  Freyberg  Process, 31 

Extraction  of  Silver  by  the  Patio  Process, 28 

Extraction  of  Silver  by  the  Yeach  Process, 32 

Extraction  of  Silver  by  the  Augustin  Process, 39 

Extraction  of  Silver  by  the  Ziervogel  Process, 42 

Extraction  of  Silver  by  the  Patera  Process,  . . .  * 43 

Flux,  Black, 21 

Flux,  White, 22 

Involution, 87 

Laws  of  Grinding, 102 

Miscellaneous  Table, 120 

Mensuration, 69 

Mechanics,  and  Mechanical  Problems, 44 

Mechanical  Powers,  viz.  : 59 

The  Lever, 59 

The  Pulley, 6» 

The  Inclined  Plane, 60 

Mechanical  Problems, 61-69 

Plates,  Grinding  effects  of,  viz.  : 66-69 

Conical, 107 

Plane  Circular, 107-108 

Randall's  Patent, 112 

Tractory  Conoidal 106 

Purification  of  Mercury, 25 

Preface, 3 

Properties  of  Bodies,  Table  of 117 

Recipes — Chemicals  employed  in  Silver  Mining, 34 

Recapitulation  of  the  Grinding  effects  of  differently  formed 

Plates, 115 

Quicksilvering  of  Copper  Plate, 23 


129 


Roasting,  viz. : 23 

In  Heaps, 23 

In  Furnaces, 23 

In  Reverberatory  Furnaces, 24 

Steam  Power, 53 

Solders, 22 

Separation  of  Silver  from  Lead  by  the  Pattinson  Process, .  35 

Separation  of  Silver  from  Lead  by  the  Parke  Process, ....  37 

Separation  of  Silver  from  Lead  by  Cupellation, 38 

Suspension  Rods  of  Uniform  Strength, 64 

Separation  of  Silver  from  Copper  by  the  Liquation  Process  36 
Table  of  Coefficients  for  estimating  the  Horse  Power  of 

Water  Wheels, 52 

Table  showing  the   Average  efficiency  of  various  Water 

Wheels, 50 

Table  showing  the  proper  velocity  of  Water  Wheels, 51 

Table  of  Pressures,  Temperatures  and  Volumes, 54 

Table  for  estimating  the  Mean  Pressures  of  Steam  for  a 

given  Cut-off  of  Stroke, 55 

Table,  Tractory 100 

Tests,  Chemical '. 10 

To  find  the  Mean  Pressure  of  Steam  for  a  given  Cut-off  of 

Stroke, 57 

To  find  the  effective  Horse  Power  of  a  Non-  Condensing 

Engine,  Rule, 58 

To  find  the  Horse  Power  for  various  Water  Wheels,  Rule.  52 

Thin  Cylinders, 61 

Thick  Hollow  Cylinders, ,62 

To  find  the  Grinding  effects  of 

Plane  Circular  Plates,  Rule, 66 

Conical  Plates,  Rule, 67 

Tractory  Conoidal,  Rule, 68 

Table  of  Regular  Polygons,  etc, 76 

Table  of  Regular  Polyedrons, 85 

p5 


130  INDEX. 

To  find  the  Area  of  the  Meridian  Tractory  Plane,  etc 97 

To  find  the  Surface  of  Revolution  of  the  Tractory  Conoid.  99 

To  find  the  Solid  Contents  of  the  Tractory  Conoid, 99 

To  construct  the  Tractory,  etc., 101 

To  determine  the  Solidity  of  a  Hollow  Tractory  Conoid,. .  105 

To  extract  any  Root  of  a  Power  or  Quantity, 89 

Varied  Motion, 46 

Water  Power, 49 

Water  Pipes, 65 

Weights  and  Measures, 121 


ERRATA. 


17th  Page,  26th  line. — After  the  word  "acid,"  add  dilute  and 

filter. 
28th  page,  17th  line. — For  "chloride"  read  chlorine. 

Add  the  word  filled  after  "cisterns." 

For  "Jouval"  read  Jonval. 

After  the  word  "feet"  add  the  head  being 
2  feet  3  inches. 

For  "Quality,"  read  Quantity. 

For   "Catenary,"   read    Involute  of  the 
Catenary. 

For  "or  AX,"  read  on  AX. 

For  "distruction,"  read  destruction. 

For  *'uniie,"  read  unit. 

For  "passes,"  read  possess. 

For  "Conoidal,"  read  Conoid. 


28th     " 

19th 

50th     " 

25th 

53d      " 

2d 

89th     " 

5th 

93d      " 

13th 

101st     " 

11th 

102d      " 

23d 

102d      " 

10th 

104  th     " 

12th 

106th     " 

9th 

f6 


WHEELER'S 

AMALGAMATOR. 


^^.TEnSTTEID     DEO.     1803- 


This  favorite  Amalgamator  has  recently  been  greatly 
simplified  and  improved. 

Over  three  hundred  of  these  Machines  are  now  in 
successful  operation,  and  giving  entire  satisfaction,  in 
California,  Nevada,  Mexico,  Idaho,  Colorado  and  Lower 
California. 

Further  comments  are  unnecessary. 

MANUFACTURED     AT 

MINERS*  FOUNDRY San  Francisco. 

PACIFIC  IRON  WORKS 

UNION  IRON  WORKS 

GOLDEN  STATE  IRON  W'KS  .  " 

MARYS VILLE  FOUNDRY Marysville 

P.  W.  GATES  &  CO Chicago,  III 

WHEELER  &  RANDALL. 

SAN  FRANCISCO,  June  13, 1865, 


THE 

WHEELER  &  RANDALL 

Grinder  and  Amalgamator. 

In  the  engraving  on  the  opposite  page,  A  represents  the  Tiim  of  the 
Pan;  B,  Cross  Frame;  C,  Legs  ;  D,  Gear ;  G,  Driving  Pulley ;  H, 
Muller  ;  I,  Driver  ;  K,  Dies  ;  L,  Shoes  ;  M,  Hand  Wheel  ;  N,  Jam 
Nut,  and  O,  Wiugs  or  Guide  Plates. 


The  attention  of  the  Public  is  respectfully  called  to  these 
facts  : 

1st.  That  the  Mechanical  work  accomplished  by  differently 
formed  grinding  plates,  having  the  same  diameter,  weight,  hard- 
ness, and  revolving  at  the  same  velocity,  is  as  follows,  to  wit : 

The  Mechanical  Work  of  plane,  circular  plates  of  the  usual 
ring  form,  is  ninety-eight 98 

The  Mechanical  work  of  conical  plates  of  the  most  approved 
form,  is  one  hundred  and  ten 110 

The  Mechanical  work  of  Tractory-formed  plates,  as  introduced 
in  the  invention  of  Wheeler  &  Randall,  is  one  hundred  and 
seventy-seven .177 

That  is,  the  Tractory-formed  grinding  plates  will  reduce  one 
hundred  and  seventy-seven  tons  of  ore,  the  conical  grinding  plates 
one  hundred  and  ten  tons,  and  the  plane  circular  grinding  plates 
ninety-eight  tons,  to  the  same  degree  of  fineness  in  the  same  time. 
Those  using  this  invention  certify  that  they  thoroughly  reduce 
five  tons  of  ore,  as  it  ordinarily  comes  from  the  wet  battery,  per 
day  in  each  pan,  four  feet  diameter,  the  muller  making  sixty-five 
revolutions  per  minute. 

2d.  That  as  a  whole,  the  Wheeler  &  Randall  Grinder  and  Amal- 
gamator is  one  of  the  most  simple,  compact,  substantial,  conve- 
nient and  efficient  pans  in  use. 

K^  Patent  applied  for. 

MANUFACTURED  AT 

GOLDEN  STATE  IRON  WORKS San  Francisco. 

UNION  IRON  WORKS 

MINERS'  FOUNDRY " 

SAN  FRANCISCO  FOUNDRY " 

PRESCOTT  &  SCHEIDEL Marysville. 

OREGON  IRON  WORKS Portland,  Oregon. 

WHEELEE  &  RANDALL,  Inventors. 

San  Francisco,  June  13, 1865. 


THE  EXCELSIOR 

mnm  m  mmmhm* 


In  the  engraving;  on  the  opposite  page.  A  represents  the  Rim  of  the 
Pan  ;  B,  Muller  ;  C,  Legs  ;  D,  Cross-Frame;  E,  Gearing  ;  F,  Screw  ; 
G,  Lever  ;  H,  Dash-Boards  ;  I,  Key  ;  a,  Dies  ;  c,  Shoes,  and  o, 
Openings, 

»  .+.  , 

The  relative  grinding  capacities  of  "The  Excelsior"  Grinder 
and  Amalgamator,  of  the  Flat  Bottomed  Pan,  and  of  the  Conical 
Pan  when  properly  constructed,  are  respectively  177,  98  and  110. 

That  is,  the  respective  mailers  being  of  the  same  diameter, 
same  weight,  same  hardness,  and  running  at  the  same  velocity, 
"The  Excelsior  Grinder  and  Amalgamator"  will  reduce  one  hun- 
dred and  seventy-seven  tons  of  ore,  the  Flat  Bottomed  Pan  ninety- 
eight  tons,  and  the  Conical  Pan  one  hundred  and  ten  tons  to  the 
same  degree  of  fineness  in  the  same  time. 

The  wear  to  the  Shoes  and  Dies  at  their  grinding  surfaces  in  the 
Excelsior  Grinder  and  Amalgamator,  is  perfectly  uniform,  thus 
securing  evenness  of  reduction  to  the  pulp,  as  well  as  steadiness 
of  motion  to  the  muller.  Uniform  wear  of  the  grinding  plates 
has  been  attained  in  no  other  than  that  of  the  Tractory  form — nor 
can  it  be. 

Another  property  of  excellence  in  this  machine  is  that  the  metal 
or  substance  to  be  amalgamated  passes  direct  from  the  grinding 
surfaces  into  the  quicksilver ;  thus  excluding  the  possibility  of  its 
becoming  coated  with  any  foreign  substances,  after  having  been 
burnished.  It  is  truthfully  said  "that  the  Tractory-formed  Pan 
as  a  Grinder  has  no  equal,  and  as  an  Amalgamator  no  superior." 

As  a  whole,  it  is  far  superior  to  any  other  pan  in  use. 

MANUFACTURED  AT  THE 

Union  Iron  Works  and  Golden  State  Iron  Works, 
WHEELER  &  RANDALL,  Inventors. 


The  undersigned  having  had  several  years  of  experience  in  practical 
quartz  mining  operations,  will  ever  take  great  pleasure  in  furnishing 
parties  interested  in  mining  and  machinery  any  desired  information 
which  they  may  possess. 

WHEELER  &  RANDALL. 

San  Francisco,  June  13, 1865. 


Q.  W.  PRESCOTT.  CHAS.  W.  SCHEIDEL. 

MARYSYILLE  FOUNDRY 

AND 

3JCacliino   Shop. 

CORNER  FOURTH  AND  B   STREETS, 

MARYSVILLE. 


The  above  Establishment  has  been  in  successful  operation  for  the 
last  twelve  years.  Having  superior  tools  for  manufacturing  and 
finishing,  and  greatly  increased  their  STOCK  OF  PATTERNS,  the 
undersigned  are  now  prepared  to  supply  all  demands  for 

MACHINERY   AND   CASTINGS, 

3f  every  description,  at  as  LOW  RATES  as  any  Foundry  in  the  State. 


STEAM   ENGINES   BUILT  AND  REPAIRED. 

Quartz  Mills,  Saw  Mills,  Grist  Mills,  Threshing  Machines 

HORSE     POWERS, 

MALT   ROLLERS,   CAST  IRON  RIFFLES,  AND 
GEARING    OF    ALL   KINDS. 

We  have  Sixteen  Steam  Engines  For  Snle,  of  our  own  manu- 
facture, from  8  to  100  horse  power,  and  will  be  furnished  with  Boilers 
and  Fixtures  complete. 

AMALGAMATING   MACHINERY, 

Of  every  description,  with  all  the  Latest  Improvements. 
WHEELER  &    RANDALL  PANS, 

WHEELER  PANS  AND  SEPARATORS, 
AMALGAMATING  TUBS, 

Car  wheels,  Derricks,  etc.  etc. 


mining     :f>tt:m::e*  s. 

CORNISH  PUMPS  of  all  sizes,  with  Gearing  and  Pipes 
made  to  order. 
HOISTING  MACHINERY,  for  Shafts  or  Inclines  of  every  variety. 
We  are  sole  manufacturers  for  the  State  of  California  of 

WINHAM'S  HYDKAT7LIC  COUPLING. 
All  orders  promptly  filled  at  the  shortest  notice,  and  at  reduced 
prices  for  cash. 

PRESCOTT  &  SCIIEIDEC 


A.  C.  GIBBS JOHN    NATION E.  S  MORGAN. 


A.  C.  GIBBS  &  CO. 

MANUFACTURERS  OF 

STEAM  EN(HNES,B0ILER8 

AND  ALL  KINDS  OF  MILLS. 

*    it  * 


®M  Separators 

OF  THE  MOST  APPROVED  KINDS. 

COOKING  RANGES,  PUMPS,  ETC.,  ETC. 

HP5*  PATTERN  MAKING  in  all  its  forms  connected  with  the 
Establishment. 

03*-  Plans  and  Specifications  for  Mills  and  all  kinds  of 
Machinery  furnished  to  order,  by  an  experienced  Draughtsman. 


THE  WHEELER  &  RANDALL 

&riad$r  tit)  Amalgamator. 


GOLDEN  STATE 

Iron    Works, 

PALMER,  KNOX  &  CO.  Proprietors, 

MANUFACTURE  ALL  KINDS  OF 

CASTINGS    AND   MACHINERY 

Best  Adapted  to  Mining  and  Milling. 

QUARTZ    MILLS,  combining  all  improvements  made  to 
date. 

STEAM  ENGINES  of  all  sizes. 

WHEELER  &  RANDALL'S  GRINDING  AND  AMALGAMATING  PANS. 

KNOX'S  AMALGAMATORS,  with  Palmer's  Steam  Chest. 
HANSCOM'S    CRUSHERS,  designed  to  prepare  Ore  for 
batteries. 

TYLER'S  PATENT  IMPROVED  WATER  WHEEL. 
DUNBAR'S  PATENT  PISTON  PACKING. 


A  FULL  SUPPLY  of  WHITE  IRON  CONSTANTLY  ON  HAND. 


Parties  desiring  anything  in  our  line,  are  invited  to  a  personal 
interview,  or  to  communicate  by  letter. 

Nos.  19,  21,  23,  25  &27  First  Street, 

SAN     FRANCISCO, 


UNION  IRON  WORKS. 


HENRY  J.  BOOTH. .  .GEO.  W.  PRESCOTT. .  .IRVING  M.  SCOTT 


H.  J.  BOOTH  &  CO. 

MANUFACTURERS  OF 

(L<d©©qctj©$w©j>  S$atp5m©i>  acn^l  StftttofUMTjf  dKg'S^os. 

FLUE,  TUBULAR,  CORNISH,  AND 

MARINE  BOILERS. 

HOISTING    MACHINES, 
PUMPS   AND  PUMPING  MACHINERY, 

ALL   KINDS    OF 

STAMPS  and  MORTARS,  AMALGAMATING 
PANS    AND    SEPARATORS, 

Of  the  most  Improved  Patterns. 
ALL     KUN-IDS     OF      SOIRJBEISrS, 


PATTERNS  AND  PATTERN  MAKING, 

OF  ALL  KINDS,  CARRIED    OX. 

PLANS  and  SPECIFICATIONS  for  Mills  and  all  kinds  of 
Machinery  furnished  free  of  cost. 

H.  J.  BOOTH  &  CO. 

FIRST  STREET,  Between  Market  and  Mission, 
SAN   FRANCISCO. 


WHEELER  &  RANDALL'S 


ZEN.AS  WHEELER'S 
Patent  Self-Regulating 

QUICKSILVER  DISCHARGE  APPARATUS. 


The  structure  of  this  Machine  is  simple  and  sub- 
stantial. Its  practical  workings  complete,  requiring  but 
little  attention. 

...*  Its  superior  settling  properties  are  readily  acknow- 
ledged by  the  most  intelligent  and  practical  amalga- 
mators and  millsmen. 

WHEELEE  &  RANDALL, 

Inventors. 


fpimjj  mi  $ tkntxlu  gta*; 

PUBLISHED  EVERY  SATURDAY  BY 

PATENT  AGENTS, 

No.  505  Clay  Street,  corner  of  Sansome, 

SAN     FRANCISCO. 


Each  number  of  the  Press  contains  sixteen  pages  of  sixty-four 
columns,  (size  of  Harper's  Weekly,)  embracing-  a  variety  of  reading 
of  direct  value  to  the  progressive  citizens  of  the  Pacific  Coast.  Our 
columns  contain  a  liberal  discussion  of  the  different  methods  of 

s.A/vi3sra-    g-old, 

All  new  discoveries  in  the  treatment  and  development  of  precious 
ores  and  metals,  and  illustrations  of  new  machinery  and  inventions. 
Commencement  of  Eleventh  Volume,  July  8th,  1865. 

Terms,  in  Advance.— One  year,  $5  ;  six  months,  $3.  Back  vol- 
umes, to  January  1,  1864,  furnished  at  $3  per  volume. 

OUR    PATENT    AGENCY 

Is  conducted  in  a  competent,  thorough,  reliable  and  strictly  confiden- 
tial manner.  Inventors  on  this  coast  having  their  applications  for 
patents  made  out  through  our  Agency,  can  sign  their  papers  at  once, 
and  thus  secure  their  rights  at  least  three  months  earlier  than  by 
trusting  the  same  to  distant  agencies,  situated  in  New  York  or 
Washington. 


Job     IPr-inting-. 

We  have  a  large  and  well  established  Office  for  BOOK  AND  JOB 
PRINTING — in  Plain,  Fancy  and  Ornamental  Style.  Especial  atten- 
tion given  to  ail  work  for  Mining  Companies  and  managers. 

*&■  Prices   ULiOXTC".  -«* 


